diff --git a/doc/pub/week35/html/._week35-bs010.html b/doc/pub/week35/html/._week35-bs010.html
index 408f18d6c..eb91dd405 100644
--- a/doc/pub/week35/html/._week35-bs010.html
+++ b/doc/pub/week35/html/._week35-bs010.html
@@ -380,7 +380,7 @@ $$
 
 <p>with \( \boldsymbol{y} \) a vector of length \( m \), \( \boldsymbol{A} \) an \( m\times n \) matrix and \( \boldsymbol{x} \) a vector of length \( n \). We assume also that \( \boldsymbol{A} \) does not depend on any of the two vectors.
 In order to find the derivative of \( \alpha \) with respect to the two vectors, we define an intermediate vector \( \boldsymbol{z} \). We define first
-\( \boldsymbol{z}^T=\boldsymbol{y}^T\boldsymbol{A} \), a vector of length \( n \). We have then
+\( \boldsymbol{z}^T=\boldsymbol{y}^T\boldsymbol{A} \), a vector of length \( n \). We have then, using the definition of the Jacobian,
 </p>
 $$
 \alpha = \boldsymbol{z}^T\boldsymbol{x},
@@ -388,9 +388,11 @@ $$
 
 <p>which means that (using our previous example) we have</p>
 $$
-\frac{\partial \alpha}{\partial \boldsymbol{x}} = \boldsymbol{z}^T=\boldsymbol{y}^T\boldsymbol{A}.
+\frac{\partial \alpha}{\partial \boldsymbol{x}} = \boldsymbol{z}=bm{A}^T\boldsymbol{y}.
 $$
 
+<p>Note that the resulting vector elements are the same for \( \boldsymbol{z}^T \) and \( \boldsymbol{z} \), the only difference is that one if just the transpose of the other.</p>
+
 <p>Since \( \alpha \) is a scalar we have \( \alpha =\alpha^T=\boldsymbol{x}^T\boldsymbol{A}^T\boldsymbol{y} \). Defining now \( \boldsymbol{z}=\boldsymbol{x}^T\boldsymbol{A}^T \) we find that</p>
 $$
 \frac{\partial \alpha}{\partial \boldsymbol{y}} = \boldsymbol{z}^T=\boldsymbol{x}^T\boldsymbol{A}^T.
diff --git a/doc/pub/week35/html/week35-reveal.html b/doc/pub/week35/html/week35-reveal.html
index cb595855f..42d1a5b03 100644
--- a/doc/pub/week35/html/week35-reveal.html
+++ b/doc/pub/week35/html/week35-reveal.html
@@ -530,7 +530,7 @@ $$
 
 <p>with \( \boldsymbol{y} \) a vector of length \( m \), \( \boldsymbol{A} \) an \( m\times n \) matrix and \( \boldsymbol{x} \) a vector of length \( n \). We assume also that \( \boldsymbol{A} \) does not depend on any of the two vectors.
 In order to find the derivative of \( \alpha \) with respect to the two vectors, we define an intermediate vector \( \boldsymbol{z} \). We define first
-\( \boldsymbol{z}^T=\boldsymbol{y}^T\boldsymbol{A} \), a vector of length \( n \). We have then
+\( \boldsymbol{z}^T=\boldsymbol{y}^T\boldsymbol{A} \), a vector of length \( n \). We have then, using the definition of the Jacobian,
 </p>
 <p>&nbsp;<br>
 $$
@@ -541,10 +541,12 @@ $$
 <p>which means that (using our previous example) we have</p>
 <p>&nbsp;<br>
 $$
-\frac{\partial \alpha}{\partial \boldsymbol{x}} = \boldsymbol{z}^T=\boldsymbol{y}^T\boldsymbol{A}.
+\frac{\partial \alpha}{\partial \boldsymbol{x}} = \boldsymbol{z}=bm{A}^T\boldsymbol{y}.
 $$
 <p>&nbsp;<br>
 
+<p>Note that the resulting vector elements are the same for \( \boldsymbol{z}^T \) and \( \boldsymbol{z} \), the only difference is that one if just the transpose of the other.</p>
+
 <p>Since \( \alpha \) is a scalar we have \( \alpha =\alpha^T=\boldsymbol{x}^T\boldsymbol{A}^T\boldsymbol{y} \). Defining now \( \boldsymbol{z}=\boldsymbol{x}^T\boldsymbol{A}^T \) we find that</p>
 <p>&nbsp;<br>
 $$
diff --git a/doc/pub/week35/html/week35-solarized.html b/doc/pub/week35/html/week35-solarized.html
index 9308cb802..1e0c3bb46 100644
--- a/doc/pub/week35/html/week35-solarized.html
+++ b/doc/pub/week35/html/week35-solarized.html
@@ -602,7 +602,7 @@ $$
 
 <p>with \( \boldsymbol{y} \) a vector of length \( m \), \( \boldsymbol{A} \) an \( m\times n \) matrix and \( \boldsymbol{x} \) a vector of length \( n \). We assume also that \( \boldsymbol{A} \) does not depend on any of the two vectors.
 In order to find the derivative of \( \alpha \) with respect to the two vectors, we define an intermediate vector \( \boldsymbol{z} \). We define first
-\( \boldsymbol{z}^T=\boldsymbol{y}^T\boldsymbol{A} \), a vector of length \( n \). We have then
+\( \boldsymbol{z}^T=\boldsymbol{y}^T\boldsymbol{A} \), a vector of length \( n \). We have then, using the definition of the Jacobian,
 </p>
 $$
 \alpha = \boldsymbol{z}^T\boldsymbol{x},
@@ -610,9 +610,11 @@ $$
 
 <p>which means that (using our previous example) we have</p>
 $$
-\frac{\partial \alpha}{\partial \boldsymbol{x}} = \boldsymbol{z}^T=\boldsymbol{y}^T\boldsymbol{A}.
+\frac{\partial \alpha}{\partial \boldsymbol{x}} = \boldsymbol{z}=bm{A}^T\boldsymbol{y}.
 $$
 
+<p>Note that the resulting vector elements are the same for \( \boldsymbol{z}^T \) and \( \boldsymbol{z} \), the only difference is that one if just the transpose of the other.</p>
+
 <p>Since \( \alpha \) is a scalar we have \( \alpha =\alpha^T=\boldsymbol{x}^T\boldsymbol{A}^T\boldsymbol{y} \). Defining now \( \boldsymbol{z}=\boldsymbol{x}^T\boldsymbol{A}^T \) we find that</p>
 $$
 \frac{\partial \alpha}{\partial \boldsymbol{y}} = \boldsymbol{z}^T=\boldsymbol{x}^T\boldsymbol{A}^T.
diff --git a/doc/pub/week35/html/week35.html b/doc/pub/week35/html/week35.html
index 1d054cbb3..e8dff76fd 100644
--- a/doc/pub/week35/html/week35.html
+++ b/doc/pub/week35/html/week35.html
@@ -679,7 +679,7 @@ $$
 
 <p>with \( \boldsymbol{y} \) a vector of length \( m \), \( \boldsymbol{A} \) an \( m\times n \) matrix and \( \boldsymbol{x} \) a vector of length \( n \). We assume also that \( \boldsymbol{A} \) does not depend on any of the two vectors.
 In order to find the derivative of \( \alpha \) with respect to the two vectors, we define an intermediate vector \( \boldsymbol{z} \). We define first
-\( \boldsymbol{z}^T=\boldsymbol{y}^T\boldsymbol{A} \), a vector of length \( n \). We have then
+\( \boldsymbol{z}^T=\boldsymbol{y}^T\boldsymbol{A} \), a vector of length \( n \). We have then, using the definition of the Jacobian,
 </p>
 $$
 \alpha = \boldsymbol{z}^T\boldsymbol{x},
@@ -687,9 +687,11 @@ $$
 
 <p>which means that (using our previous example) we have</p>
 $$
-\frac{\partial \alpha}{\partial \boldsymbol{x}} = \boldsymbol{z}^T=\boldsymbol{y}^T\boldsymbol{A}.
+\frac{\partial \alpha}{\partial \boldsymbol{x}} = \boldsymbol{z}=bm{A}^T\boldsymbol{y}.
 $$
 
+<p>Note that the resulting vector elements are the same for \( \boldsymbol{z}^T \) and \( \boldsymbol{z} \), the only difference is that one if just the transpose of the other.</p>
+
 <p>Since \( \alpha \) is a scalar we have \( \alpha =\alpha^T=\boldsymbol{x}^T\boldsymbol{A}^T\boldsymbol{y} \). Defining now \( \boldsymbol{z}=\boldsymbol{x}^T\boldsymbol{A}^T \) we find that</p>
 $$
 \frac{\partial \alpha}{\partial \boldsymbol{y}} = \boldsymbol{z}^T=\boldsymbol{x}^T\boldsymbol{A}^T.
diff --git a/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz b/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz
index dd8d64c65..9b781eaaf 100644
Binary files a/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz and b/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz differ
diff --git a/doc/pub/week35/ipynb/week35.ipynb b/doc/pub/week35/ipynb/week35.ipynb
index 827b5bcb8..c2d22256b 100644
--- a/doc/pub/week35/ipynb/week35.ipynb
+++ b/doc/pub/week35/ipynb/week35.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "838ddf3c",
+   "id": "2070762b",
    "metadata": {
     "editable": true
    },
@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "17b1747e",
+   "id": "3a35ce03",
    "metadata": {
     "editable": true
    },
@@ -27,7 +27,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "85eb10b9",
+   "id": "f250b29c",
    "metadata": {
     "editable": true
    },
@@ -49,7 +49,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "791bb6f2",
+   "id": "157d1840",
    "metadata": {
     "editable": true
    },
@@ -65,7 +65,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "add64c3b",
+   "id": "1f0e5f64",
    "metadata": {
     "editable": true
    },
@@ -99,7 +99,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ebd9eb0a",
+   "id": "e15c5dd7",
    "metadata": {
     "editable": true
    },
@@ -115,7 +115,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "48190fca",
+   "id": "7205f9ed",
    "metadata": {
     "editable": true
    },
@@ -127,7 +127,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a9e68bdb",
+   "id": "58035123",
    "metadata": {
     "editable": true
    },
@@ -137,7 +137,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9cd514cf",
+   "id": "5c054dc2",
    "metadata": {
     "editable": true
    },
@@ -149,7 +149,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "be58abcb",
+   "id": "1ccbf405",
    "metadata": {
     "editable": true
    },
@@ -170,7 +170,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65c81ad7",
+   "id": "4fc747be",
    "metadata": {
     "editable": true
    },
@@ -182,7 +182,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d06dd2df",
+   "id": "324815b4",
    "metadata": {
     "editable": true
    },
@@ -195,7 +195,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2b242f4c",
+   "id": "c31fc801",
    "metadata": {
     "editable": true
    },
@@ -207,7 +207,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fa4ce919",
+   "id": "5f390ec4",
    "metadata": {
     "editable": true
    },
@@ -219,7 +219,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "809bddba",
+   "id": "a7b23937",
    "metadata": {
     "editable": true
    },
@@ -229,7 +229,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c13096cd",
+   "id": "db0cea3d",
    "metadata": {
     "editable": true
    },
@@ -241,7 +241,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "51bf0ce3",
+   "id": "936418d7",
    "metadata": {
     "editable": true
    },
@@ -254,7 +254,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ebdcd499",
+   "id": "3b2a6714",
    "metadata": {
     "editable": true
    },
@@ -266,7 +266,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "052a85b8",
+   "id": "54120755",
    "metadata": {
     "editable": true
    },
@@ -276,7 +276,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7896972c",
+   "id": "f8854f6e",
    "metadata": {
     "editable": true
    },
@@ -288,7 +288,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9cb44c6e",
+   "id": "468fd216",
    "metadata": {
     "editable": true
    },
@@ -300,7 +300,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c07d6100",
+   "id": "cd5e2caa",
    "metadata": {
     "editable": true
    },
@@ -311,7 +311,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a9038b2b",
+   "id": "32e08e08",
    "metadata": {
     "editable": true
    },
@@ -323,7 +323,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ee219eaa",
+   "id": "af8df8e6",
    "metadata": {
     "editable": true
    },
@@ -342,7 +342,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4b483278",
+   "id": "89f55eba",
    "metadata": {
     "editable": true
    },
@@ -355,7 +355,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0c3695c7",
+   "id": "3594bcb9",
    "metadata": {
     "editable": true
    },
@@ -365,7 +365,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "31f3f261",
+   "id": "1e45992c",
    "metadata": {
     "editable": true
    },
@@ -377,7 +377,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8a16a039",
+   "id": "90198ba6",
    "metadata": {
     "editable": true
    },
@@ -387,7 +387,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1cae8e04",
+   "id": "78c4cc43",
    "metadata": {
     "editable": true
    },
@@ -399,7 +399,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "79352075",
+   "id": "8d138d4c",
    "metadata": {
     "editable": true
    },
@@ -409,7 +409,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0ccf5e17",
+   "id": "ba40b8d7",
    "metadata": {
     "editable": true
    },
@@ -421,7 +421,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3986d65c",
+   "id": "e8f749fe",
    "metadata": {
     "editable": true
    },
@@ -432,7 +432,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aa1d71ae",
+   "id": "c679efad",
    "metadata": {
     "editable": true
    },
@@ -444,7 +444,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "30f9467b",
+   "id": "f1aaeaca",
    "metadata": {
     "editable": true
    },
@@ -454,7 +454,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ff88b45c",
+   "id": "fd4ae817",
    "metadata": {
     "editable": true
    },
@@ -466,7 +466,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2b200f18",
+   "id": "d09f9a77",
    "metadata": {
     "editable": true
    },
@@ -476,7 +476,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e976c578",
+   "id": "09ec2766",
    "metadata": {
     "editable": true
    },
@@ -488,7 +488,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7a53072f",
+   "id": "ad758d65",
    "metadata": {
     "editable": true
    },
@@ -508,7 +508,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b254dabb",
+   "id": "9d72460a",
    "metadata": {
     "editable": true
    },
@@ -535,7 +535,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "59c29834",
+   "id": "318afac7",
    "metadata": {
     "editable": true
    },
@@ -547,7 +547,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a2dd4402",
+   "id": "e885156f",
    "metadata": {
     "editable": true
    },
@@ -559,7 +559,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "251d409a",
+   "id": "cd7e8abb",
    "metadata": {
     "editable": true
    },
@@ -575,7 +575,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a86432c8",
+   "id": "6a7946a6",
    "metadata": {
     "editable": true
    },
@@ -593,7 +593,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f52757b7",
+   "id": "bc7dac5b",
    "metadata": {
     "editable": true
    },
@@ -605,7 +605,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c2295ece",
+   "id": "fb7b7c7a",
    "metadata": {
     "editable": true
    },
@@ -617,7 +617,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "01dbc04e",
+   "id": "fdab3f90",
    "metadata": {
     "editable": true
    },
@@ -628,7 +628,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2f513341",
+   "id": "d398d440",
    "metadata": {
     "editable": true
    },
@@ -640,7 +640,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c41bbc8f",
+   "id": "f90d2059",
    "metadata": {
     "editable": true
    },
@@ -650,7 +650,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5a64d3aa",
+   "id": "3872052b",
    "metadata": {
     "editable": true
    },
@@ -662,7 +662,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3e0766a7",
+   "id": "535cf990",
    "metadata": {
     "editable": true
    },
@@ -676,7 +676,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2317828c",
+   "id": "197d3e9f",
    "metadata": {
     "editable": true
    },
@@ -688,19 +688,19 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f32112c9",
+   "id": "e2c7a4f9",
    "metadata": {
     "editable": true
    },
    "source": [
     "with $\\boldsymbol{y}$ a vector of length $m$, $\\boldsymbol{A}$ an $m\\times n$ matrix and $\\boldsymbol{x}$ a vector of length $n$. We assume also that $\\boldsymbol{A}$ does not depend on any of the two vectors.\n",
     "In order to find the derivative of $\\alpha$ with respect to the two vectors, we define an intermediate vector $\\boldsymbol{z}$. We define first\n",
-    "$\\boldsymbol{z}^T=\\boldsymbol{y}^T\\boldsymbol{A}$, a vector of length $n$. We have then"
+    "$\\boldsymbol{z}^T=\\boldsymbol{y}^T\\boldsymbol{A}$, a vector of length $n$. We have then, using the definition of the Jacobian,"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "f638dc03",
+   "id": "834ecb73",
    "metadata": {
     "editable": true
    },
@@ -712,7 +712,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4e5be62b",
+   "id": "89e5b0d3",
    "metadata": {
     "editable": true
    },
@@ -722,29 +722,31 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d7cb2146",
+   "id": "f7e022ca",
    "metadata": {
     "editable": true
    },
    "source": [
     "$$\n",
-    "\\frac{\\partial \\alpha}{\\partial \\boldsymbol{x}} = \\boldsymbol{z}^T=\\boldsymbol{y}^T\\boldsymbol{A}.\n",
+    "\\frac{\\partial \\alpha}{\\partial \\boldsymbol{x}} = \\boldsymbol{z}=bm{A}^T\\boldsymbol{y}.\n",
     "$$"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "11d5122b",
+   "id": "0f9fa0cd",
    "metadata": {
     "editable": true
    },
    "source": [
+    "Note that the resulting vector elements are the same for $\\boldsymbol{z}^T$ and $\\boldsymbol{z}$, the only difference is that one if just the transpose of the other.\n",
+    "\n",
     "Since $\\alpha$ is a scalar we have $\\alpha =\\alpha^T=\\boldsymbol{x}^T\\boldsymbol{A}^T\\boldsymbol{y}$. Defining now $\\boldsymbol{z}=\\boldsymbol{x}^T\\boldsymbol{A}^T$ we find that"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "a3ab7ada",
+   "id": "7207e78d",
    "metadata": {
     "editable": true
    },
@@ -756,7 +758,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2484de20",
+   "id": "a58d233a",
    "metadata": {
     "editable": true
    },
@@ -770,7 +772,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c05c9882",
+   "id": "08676c15",
    "metadata": {
     "editable": true
    },
@@ -782,7 +784,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "af6d440c",
+   "id": "0c4417ed",
    "metadata": {
     "editable": true
    },
@@ -794,7 +796,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "49a54935",
+   "id": "9f43d971",
    "metadata": {
     "editable": true
    },
@@ -806,7 +808,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3e1e1f54",
+   "id": "b0fc3f13",
    "metadata": {
     "editable": true
    },
@@ -816,7 +818,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e84f7a76",
+   "id": "105376e3",
    "metadata": {
     "editable": true
    },
@@ -828,7 +830,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3b454236",
+   "id": "6aa6fe7f",
    "metadata": {
     "editable": true
    },
@@ -838,7 +840,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1c9967bd",
+   "id": "7fecb158",
    "metadata": {
     "editable": true
    },
@@ -850,7 +852,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e1d22d0a",
+   "id": "d0e52ab7",
    "metadata": {
     "editable": true
    },
@@ -860,7 +862,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e9f8f1b1",
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@@ -872,7 +874,7 @@
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@@ -884,7 +886,7 @@
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@@ -896,7 +898,7 @@
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@@ -911,7 +913,7 @@
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@@ -923,7 +925,7 @@
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@@ -933,7 +935,7 @@
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@@ -945,7 +947,7 @@
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@@ -955,7 +957,7 @@
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@@ -967,7 +969,7 @@
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@@ -977,7 +979,7 @@
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@@ -989,7 +991,7 @@
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@@ -1001,7 +1003,7 @@
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@@ -1013,7 +1015,7 @@
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@@ -1023,7 +1025,7 @@
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@@ -1035,7 +1037,7 @@
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@@ -1048,7 +1050,7 @@
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@@ -1060,7 +1062,7 @@
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@@ -1070,7 +1072,7 @@
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@@ -1082,7 +1084,7 @@
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@@ -1092,7 +1094,7 @@
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@@ -1104,7 +1106,7 @@
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@@ -1114,7 +1116,7 @@
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@@ -1126,7 +1128,7 @@
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@@ -1136,7 +1138,7 @@
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@@ -1148,7 +1150,7 @@
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@@ -1158,7 +1160,7 @@
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@@ -1170,7 +1172,7 @@
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@@ -1182,7 +1184,7 @@
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@@ -1194,7 +1196,7 @@
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@@ -1206,7 +1208,7 @@
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@@ -1218,7 +1220,7 @@
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@@ -1234,7 +1236,7 @@
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@@ -1246,7 +1248,7 @@
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@@ -1256,7 +1258,7 @@
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@@ -1268,7 +1270,7 @@
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@@ -1286,7 +1288,7 @@
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@@ -1298,7 +1300,7 @@
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@@ -1310,7 +1312,7 @@
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@@ -1320,7 +1322,7 @@
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@@ -1332,7 +1334,7 @@
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@@ -1342,7 +1344,7 @@
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@@ -1354,7 +1356,7 @@
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@@ -1364,7 +1366,7 @@
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@@ -1378,7 +1380,7 @@
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@@ -1390,7 +1392,7 @@
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@@ -1401,7 +1403,7 @@
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@@ -1414,7 +1416,7 @@
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@@ -1441,7 +1443,7 @@
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@@ -1452,7 +1454,7 @@
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@@ -1465,7 +1467,7 @@
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@@ -1479,7 +1481,7 @@
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@@ -1492,7 +1494,7 @@
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@@ -1503,7 +1505,7 @@
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@@ -1515,7 +1517,7 @@
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@@ -1526,7 +1528,7 @@
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@@ -1542,7 +1544,7 @@
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@@ -1553,7 +1555,7 @@
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@@ -1567,7 +1569,7 @@
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@@ -1588,7 +1590,7 @@
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@@ -1599,7 +1601,7 @@
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@@ -1652,7 +1654,7 @@
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@@ -1663,7 +1665,7 @@
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@@ -1688,7 +1690,7 @@
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@@ -1700,7 +1702,7 @@
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@@ -1729,7 +1731,7 @@
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@@ -1754,7 +1756,7 @@
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@@ -1774,7 +1776,7 @@
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@@ -1801,7 +1803,7 @@
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@@ -1814,7 +1816,7 @@
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@@ -1826,7 +1828,7 @@
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@@ -1837,7 +1839,7 @@
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@@ -1853,7 +1855,7 @@
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@@ -1887,7 +1889,7 @@
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@@ -1897,7 +1899,7 @@
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@@ -1912,7 +1914,7 @@
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@@ -1924,7 +1926,7 @@
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@@ -1934,7 +1936,7 @@
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@@ -1950,7 +1952,7 @@
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@@ -1967,7 +1969,7 @@
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@@ -1980,7 +1982,7 @@
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@@ -2027,7 +2029,7 @@
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@@ -2038,7 +2040,7 @@
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@@ -2141,7 +2143,7 @@
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@@ -2169,7 +2171,7 @@
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@@ -2204,7 +2206,7 @@
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@@ -2219,7 +2221,7 @@
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@@ -2244,7 +2246,7 @@
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@@ -2260,7 +2262,7 @@
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@@ -2272,7 +2274,7 @@
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@@ -2287,7 +2289,7 @@
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@@ -2299,7 +2301,7 @@
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@@ -2309,7 +2311,7 @@
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@@ -2321,7 +2323,7 @@
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@@ -2331,7 +2333,7 @@
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@@ -2343,7 +2345,7 @@
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@@ -2356,7 +2358,7 @@
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@@ -2368,7 +2370,7 @@
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@@ -2378,7 +2380,7 @@
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@@ -2390,7 +2392,7 @@
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@@ -2400,7 +2402,7 @@
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@@ -2412,7 +2414,7 @@
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@@ -2422,7 +2424,7 @@
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@@ -2434,7 +2436,7 @@
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@@ -2444,7 +2446,7 @@
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@@ -2456,7 +2458,7 @@
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@@ -2466,7 +2468,7 @@
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@@ -2478,7 +2480,7 @@
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@@ -2488,7 +2490,7 @@
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@@ -2500,7 +2502,7 @@
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@@ -2512,7 +2514,7 @@
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@@ -2524,7 +2526,7 @@
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@@ -2537,7 +2539,7 @@
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@@ -2549,7 +2551,7 @@
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@@ -2559,7 +2561,7 @@
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@@ -2573,7 +2575,7 @@
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@@ -2670,7 +2672,7 @@
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@@ -2691,7 +2693,7 @@
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@@ -2703,7 +2705,7 @@
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@@ -2713,7 +2715,7 @@
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@@ -2725,7 +2727,7 @@
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@@ -2735,7 +2737,7 @@
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@@ -2747,7 +2749,7 @@
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@@ -2763,7 +2765,7 @@
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@@ -2807,7 +2809,7 @@
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@@ -2819,7 +2821,7 @@
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@@ -2835,7 +2837,7 @@
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@@ -2846,7 +2848,7 @@
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@@ -2864,7 +2866,7 @@
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@@ -2875,7 +2877,7 @@
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@@ -2889,7 +2891,7 @@
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@@ -2900,7 +2902,7 @@
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@@ -2913,7 +2915,7 @@
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@@ -2924,7 +2926,7 @@
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@@ -2941,7 +2943,7 @@
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@@ -2952,7 +2954,7 @@
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@@ -2968,7 +2970,7 @@
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@@ -2979,7 +2981,7 @@
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@@ -3003,7 +3005,7 @@
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@@ -3014,7 +3016,7 @@
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@@ -3027,7 +3029,7 @@
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@@ -3038,7 +3040,7 @@
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@@ -3058,7 +3060,7 @@
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@@ -3069,7 +3071,7 @@
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@@ -3112,7 +3114,7 @@
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@@ -3127,7 +3129,7 @@
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@@ -3137,7 +3139,7 @@
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@@ -3151,7 +3153,7 @@
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@@ -3163,7 +3165,7 @@
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@@ -3175,7 +3177,7 @@
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@@ -3187,7 +3189,7 @@
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@@ -3197,7 +3199,7 @@
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@@ -3209,7 +3211,7 @@
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@@ -3219,7 +3221,7 @@
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@@ -3231,7 +3233,7 @@
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@@ -3242,7 +3244,7 @@
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@@ -3254,7 +3256,7 @@
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@@ -3266,7 +3268,7 @@
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@@ -3276,7 +3278,7 @@
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@@ -3288,7 +3290,7 @@
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@@ -3300,7 +3302,7 @@
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@@ -3310,7 +3312,7 @@
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@@ -3322,7 +3324,7 @@
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@@ -3332,7 +3334,7 @@
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@@ -3344,7 +3346,7 @@
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@@ -3354,7 +3356,7 @@
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@@ -3394,7 +3396,7 @@
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@@ -3411,7 +3413,7 @@
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@@ -3434,7 +3436,7 @@
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@@ -3451,7 +3453,7 @@
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@@ -3470,7 +3472,7 @@
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@@ -3481,7 +3483,7 @@
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@@ -3493,7 +3495,7 @@
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@@ -3511,7 +3513,7 @@
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@@ -3527,7 +3529,7 @@
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@@ -3539,7 +3541,7 @@
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@@ -3549,7 +3551,7 @@
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@@ -3564,7 +3566,7 @@
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@@ -3576,7 +3578,7 @@
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@@ -3586,7 +3588,7 @@
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@@ -3598,7 +3600,7 @@
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@@ -3608,7 +3610,7 @@
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@@ -3620,7 +3622,7 @@
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@@ -3632,7 +3634,7 @@
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@@ -3647,7 +3649,7 @@
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@@ -3658,7 +3660,7 @@
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@@ -3678,7 +3680,7 @@
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@@ -3690,7 +3692,7 @@
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@@ -3700,7 +3702,7 @@
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@@ -3712,7 +3714,7 @@
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@@ -3741,7 +3743,7 @@
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@@ -3768,7 +3770,7 @@
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@@ -3779,7 +3781,7 @@
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-   "id": "dbf16459",
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@@ -3819,7 +3821,7 @@
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@@ -3836,7 +3838,7 @@
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@@ -3859,7 +3861,7 @@
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@@ -3873,7 +3875,7 @@
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@@ -3892,7 +3894,7 @@
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@@ -3902,7 +3904,7 @@
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@@ -3914,7 +3916,7 @@
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@@ -3928,7 +3930,7 @@
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@@ -3940,7 +3942,7 @@
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@@ -3950,7 +3952,7 @@
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@@ -3962,7 +3964,7 @@
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@@ -3979,7 +3981,7 @@
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@@ -3989,7 +3991,7 @@
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@@ -4005,7 +4007,7 @@
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@@ -4015,7 +4017,7 @@
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@@ -4031,7 +4033,7 @@
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@@ -4041,7 +4043,7 @@
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@@ -4057,7 +4059,7 @@
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@@ -4067,7 +4069,7 @@
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@@ -4084,7 +4086,7 @@
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@@ -4096,7 +4098,7 @@
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@@ -4108,7 +4110,7 @@
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@@ -4120,7 +4122,7 @@
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@@ -4130,7 +4132,7 @@
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@@ -4142,7 +4144,7 @@
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@@ -4154,7 +4156,7 @@
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@@ -4166,7 +4168,7 @@
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@@ -4176,7 +4178,7 @@
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@@ -4188,7 +4190,7 @@
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@@ -4198,7 +4200,7 @@
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@@ -4210,7 +4212,7 @@
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@@ -4224,7 +4226,7 @@
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@@ -4236,7 +4238,7 @@
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@@ -4248,7 +4250,7 @@
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@@ -4258,7 +4260,7 @@
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@@ -4270,7 +4272,7 @@
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@@ -4281,7 +4283,7 @@
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@@ -4293,7 +4295,7 @@
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@@ -4303,7 +4305,7 @@
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@@ -4315,7 +4317,7 @@
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@@ -4325,7 +4327,7 @@
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@@ -4337,7 +4339,7 @@
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@@ -4348,7 +4350,7 @@
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@@ -4360,7 +4362,7 @@
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@@ -4378,7 +4380,7 @@
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@@ -4394,7 +4396,7 @@
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@@ -4406,7 +4408,7 @@
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@@ -4418,7 +4420,7 @@
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@@ -4430,7 +4432,7 @@
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@@ -4443,7 +4445,7 @@
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@@ -4459,7 +4461,7 @@
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@@ -4473,7 +4475,7 @@
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@@ -4483,7 +4485,7 @@
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@@ -4495,7 +4497,7 @@
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@@ -4505,7 +4507,7 @@
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@@ -4517,7 +4519,7 @@
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@@ -4527,7 +4529,7 @@
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@@ -4541,7 +4543,7 @@
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@@ -4558,7 +4560,7 @@
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@@ -4574,7 +4576,7 @@
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@@ -4586,7 +4588,7 @@
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@@ -4599,7 +4601,7 @@
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@@ -4613,7 +4615,7 @@
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@@ -4623,7 +4625,7 @@
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@@ -4636,7 +4638,7 @@
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@@ -4655,7 +4657,7 @@
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@@ -4667,7 +4669,7 @@
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@@ -4679,7 +4681,7 @@
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@@ -4689,7 +4691,7 @@
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@@ -4701,7 +4703,7 @@
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@@ -4714,7 +4716,7 @@
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@@ -4733,7 +4735,7 @@
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@@ -4743,7 +4745,7 @@
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@@ -4762,7 +4764,7 @@
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@@ -4780,7 +4782,7 @@
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@@ -4794,7 +4796,7 @@
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@@ -4809,7 +4811,7 @@
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@@ -4830,7 +4832,7 @@
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@@ -4847,7 +4849,7 @@
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@@ -4879,7 +4881,7 @@
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@@ -4893,7 +4895,7 @@
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@@ -4906,7 +4908,7 @@
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@@ -4931,7 +4933,7 @@
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@@ -4941,7 +4943,7 @@
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@@ -4952,7 +4954,7 @@
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@@ -5006,7 +5008,7 @@
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@@ -5023,7 +5025,7 @@
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@@ -5035,7 +5037,7 @@
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@@ -5047,7 +5049,7 @@
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@@ -5057,7 +5059,7 @@
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@@ -5074,7 +5076,7 @@
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@@ -5084,7 +5086,7 @@
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@@ -5099,7 +5101,7 @@
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@@ -5109,7 +5111,7 @@
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@@ -5123,7 +5125,7 @@
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@@ -5135,7 +5137,7 @@
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@@ -5147,7 +5149,7 @@
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@@ -5159,7 +5161,7 @@
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@@ -5169,7 +5171,7 @@
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@@ -5181,7 +5183,7 @@
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@@ -5191,7 +5193,7 @@
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@@ -5208,7 +5210,7 @@
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@@ -5218,7 +5220,7 @@
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@@ -5230,7 +5232,7 @@
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@@ -5240,7 +5242,7 @@
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@@ -5252,7 +5254,7 @@
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@@ -5266,7 +5268,7 @@
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@@ -5278,7 +5280,7 @@
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@@ -5300,7 +5302,7 @@
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@@ -5312,7 +5314,7 @@
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-   "id": "e9d15eae",
+   "id": "7bc685b4",
    "metadata": {
     "editable": true
    },
@@ -5327,7 +5329,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bbbc3b4e",
+   "id": "e5f74689",
    "metadata": {
     "editable": true
    },
@@ -5339,7 +5341,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "62b0fce6",
+   "id": "88c544a8",
    "metadata": {
     "editable": true
    },
@@ -5351,7 +5353,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0aa2e137",
+   "id": "8bd0dbe9",
    "metadata": {
     "editable": true
    },
@@ -5361,7 +5363,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fd93daa8",
+   "id": "42f1768e",
    "metadata": {
     "editable": true
    },
@@ -5373,7 +5375,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6cea7d7f",
+   "id": "ebfdc4f3",
    "metadata": {
     "editable": true
    },
@@ -5383,7 +5385,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0a05b8d7",
+   "id": "101ad94b",
    "metadata": {
     "editable": true
    },
@@ -5395,7 +5397,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "655a918b",
+   "id": "0bdd520e",
    "metadata": {
     "editable": true
    },
@@ -5405,7 +5407,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8f6c74f1",
+   "id": "5bbf13b1",
    "metadata": {
     "editable": true
    },
@@ -5417,7 +5419,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5b9725b2",
+   "id": "85a38e8d",
    "metadata": {
     "editable": true
    },
@@ -5434,7 +5436,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2be4cb9d",
+   "id": "f6666263",
    "metadata": {
     "editable": true
    },
@@ -5447,7 +5449,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dcc582e7",
+   "id": "587b2ce3",
    "metadata": {
     "editable": true
    },
@@ -5459,7 +5461,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5a1ed82a",
+   "id": "c22c9ddb",
    "metadata": {
     "editable": true
    },
@@ -5469,7 +5471,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c224353e",
+   "id": "7724b145",
    "metadata": {
     "editable": true
    },
@@ -5482,7 +5484,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ae79a666",
+   "id": "ec8b96ea",
    "metadata": {
     "editable": true
    },
@@ -5492,7 +5494,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "870f7011",
+   "id": "3d2a045a",
    "metadata": {
     "editable": true
    },
@@ -5504,7 +5506,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1ec298b0",
+   "id": "1056995d",
    "metadata": {
     "editable": true
    },
@@ -5517,7 +5519,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d0c145fd",
+   "id": "fef60cc6",
    "metadata": {
     "editable": true
    },
@@ -5530,7 +5532,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "086c19c7",
+   "id": "a0f33fda",
    "metadata": {
     "editable": true
    },
@@ -5542,7 +5544,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "77e6f6ae",
+   "id": "b2581a7a",
    "metadata": {
     "editable": true
    },
@@ -5554,7 +5556,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6ea94ce0",
+   "id": "e4f2ab2e",
    "metadata": {
     "editable": true
    },
@@ -5564,7 +5566,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "75fe3e7e",
+   "id": "123fb750",
    "metadata": {
     "editable": true
    },
@@ -5577,7 +5579,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b44ad029",
+   "id": "b1d58fbe",
    "metadata": {
     "editable": true
    },
@@ -5589,7 +5591,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5a6cadf4",
+   "id": "5f0259bc",
    "metadata": {
     "editable": true
    },
@@ -5601,7 +5603,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "983dd769",
+   "id": "c8fb5772",
    "metadata": {
     "editable": true
    },
@@ -5613,7 +5615,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "670240ea",
+   "id": "9f73c308",
    "metadata": {
     "editable": true
    },
@@ -5625,7 +5627,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "21222a56",
+   "id": "ac9096ce",
    "metadata": {
     "editable": true
    },
@@ -5639,7 +5641,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0a6658cf",
+   "id": "ca0b1176",
    "metadata": {
     "editable": true
    },
@@ -5651,7 +5653,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "11916659",
+   "id": "c30835a6",
    "metadata": {
     "editable": true
    },
@@ -5661,7 +5663,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f657be21",
+   "id": "ab6bb533",
    "metadata": {
     "editable": true
    },
@@ -5673,7 +5675,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d97516b8",
+   "id": "53b92c21",
    "metadata": {
     "editable": true
    },
@@ -5685,7 +5687,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "99bd354d",
+   "id": "4667c501",
    "metadata": {
     "editable": true
    },
@@ -5697,7 +5699,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "90658f5b",
+   "id": "a5f83360",
    "metadata": {
     "editable": true
    },
@@ -5709,7 +5711,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fc998d60",
+   "id": "cd2e2e5e",
    "metadata": {
     "editable": true
    },
@@ -5721,7 +5723,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6925d765",
+   "id": "c9dc1a87",
    "metadata": {
     "editable": true
    },
@@ -5740,7 +5742,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "97ff8669",
+   "id": "a948cd9f",
    "metadata": {
     "editable": true
    },
@@ -5752,7 +5754,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bfcb6e0f",
+   "id": "48e29bd0",
    "metadata": {
     "editable": true
    },
@@ -5762,7 +5764,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e2a9c918",
+   "id": "58ee4e46",
    "metadata": {
     "editable": true
    },
@@ -5774,7 +5776,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "507de073",
+   "id": "ced911f5",
    "metadata": {
     "editable": true
    },
@@ -5784,7 +5786,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "06c889f9",
+   "id": "3330c263",
    "metadata": {
     "editable": true
    },
@@ -5796,7 +5798,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fccfc919",
+   "id": "d8e1460a",
    "metadata": {
     "editable": true
    },
@@ -5808,7 +5810,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d814818f",
+   "id": "55e47a8d",
    "metadata": {
     "editable": true
    },
@@ -5824,7 +5826,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bbcc18c6",
+   "id": "4b71f3a0",
    "metadata": {
     "editable": true
    },
@@ -5836,7 +5838,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1487ed01",
+   "id": "a115cebf",
    "metadata": {
     "editable": true
    },
@@ -5848,7 +5850,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f74e089e",
+   "id": "c4d6028a",
    "metadata": {
     "editable": true
    },
@@ -5858,7 +5860,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "abd8519b",
+   "id": "98044bee",
    "metadata": {
     "editable": true
    },
@@ -5870,7 +5872,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "14effb67",
+   "id": "e3534bc0",
    "metadata": {
     "editable": true
    },
@@ -5880,7 +5882,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ba6e6ea3",
+   "id": "99bb4cd3",
    "metadata": {
     "editable": true
    },
@@ -5892,7 +5894,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "78202454",
+   "id": "88fc3c52",
    "metadata": {
     "editable": true
    },
@@ -5909,7 +5911,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f27b566a",
+   "id": "c05ba72d",
    "metadata": {
     "editable": true
    },
@@ -5921,7 +5923,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5e9449c1",
+   "id": "75da5d5a",
    "metadata": {
     "editable": true
    },
@@ -5933,7 +5935,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d425f456",
+   "id": "fcea82a3",
    "metadata": {
     "editable": true
    },
@@ -5943,7 +5945,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "71664ae1",
+   "id": "96a7a03e",
    "metadata": {
     "editable": true
    },
@@ -5955,7 +5957,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "18bc0e49",
+   "id": "4091e1b7",
    "metadata": {
     "editable": true
    },
@@ -5965,7 +5967,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "29b8cc98",
+   "id": "ded3ce7d",
    "metadata": {
     "editable": true
    },
@@ -5977,7 +5979,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a29dc217",
+   "id": "cff51920",
    "metadata": {
     "editable": true
    },
@@ -5987,7 +5989,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4d51ed4e",
+   "id": "262759a7",
    "metadata": {
     "editable": true
    },
@@ -5999,7 +6001,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c0cca566",
+   "id": "d927c104",
    "metadata": {
     "editable": true
    },
diff --git a/doc/src/week35/week35.do.txt b/doc/src/week35/week35.do.txt
index dc0033767..017da2ae6 100644
--- a/doc/src/week35/week35.do.txt
+++ b/doc/src/week35/week35.do.txt
@@ -317,7 +317,7 @@ multiplications
 !et
 with $\bm{y}$ a vector of length $m$, $\bm{A}$ an $m\times n$ matrix and $\bm{x}$ a vector of length $n$. We assume also that $\bm{A}$ does not depend on any of the two vectors.
 In order to find the derivative of $\alpha$ with respect to the two vectors, we define an intermediate vector $\bm{z}$. We define first
-$\bm{z}^T=\bm{y}^T\bm{A}$, a vector of length $n$. We have then
+$\bm{z}^T=\bm{y}^T\bm{A}$, a vector of length $n$. We have then, using the definition of the Jacobian,
 !bt
 \[
 \alpha = \bm{z}^T\bm{x},
@@ -326,10 +326,12 @@ $\bm{z}^T=\bm{y}^T\bm{A}$, a vector of length $n$. We have then
 which means that (using our previous example) we have
 !bt
 \[
-\frac{\partial \alpha}{\partial \bm{x}} = \bm{z}^T=\bm{y}^T\bm{A}.
+\frac{\partial \alpha}{\partial \bm{x}} = \bm{z}=bm{A}^T\bm{y}.
 \]
 !et
 
+Note that the resulting vector elements are the same for $\bm{z}^T$ and $\bm{z}$, the only difference is that one if just the transpose of the other.
+
 Since $\alpha$ is a scalar we have $\alpha =\alpha^T=\bm{x}^T\bm{A}^T\bm{y}$. Defining now $\bm{z}=\bm{x}^T\bm{A}^T$ we find that
 !bt
 \[