diff --git a/doc/pub/week35/html/._week35-bs000.html b/doc/pub/week35/html/._week35-bs000.html
index 5bd60570c..f39c54f6b 100644
--- a/doc/pub/week35/html/._week35-bs000.html
+++ b/doc/pub/week35/html/._week35-bs000.html
@@ -404,7 +404,7 @@ MathJax.Hub.Config({
-Aug 28, 2022
+Aug 29, 2022
diff --git a/doc/pub/week35/html/._week35-bs069.html b/doc/pub/week35/html/._week35-bs069.html
index cb9194933..951591146 100644
--- a/doc/pub/week35/html/._week35-bs069.html
+++ b/doc/pub/week35/html/._week35-bs069.html
@@ -964,6 +964,31 @@ $$
and finally find the second derivative of this function with respect to the vector \( \boldsymbol{s} \).
+Hint: In these exercises it is always useful to write out with summation indices the various quantities.
+As an example, consider the function
+
+
+$$
+f(\boldsymbol{x}) =\boldsymbol{A}\boldsymbol{x},
+$$
+
+which reads for a specific component \( f_i \) (we define the matrix \( \boldsymbol{A} \) to have dimension \( n\times n \) and the vector $\boldsymbol{x} to have length \( n \))
+
+$$
+f_i =\sum_{j=0}^{n-1}a_{ij}x_j,
+$$
+
+which leads to
+$$
+\frac{\partial f_i}{\partial x_j}= a_{ij},
+$$
+
+and written out in terms of the vector \( \boldsymbol{x} \) we have
+$$
+\frac{\partial f(\boldsymbol{x})}{\partial \boldsymbol{x}}= \boldsymbol{A}.
+$$
+
+
diff --git a/doc/pub/week35/html/week35-bs.html b/doc/pub/week35/html/week35-bs.html
index 5bd60570c..f39c54f6b 100644
--- a/doc/pub/week35/html/week35-bs.html
+++ b/doc/pub/week35/html/week35-bs.html
@@ -404,7 +404,7 @@ MathJax.Hub.Config({
-Aug 28, 2022
+Aug 29, 2022
diff --git a/doc/pub/week35/html/week35-reveal.html b/doc/pub/week35/html/week35-reveal.html
index bc3071e19..8cd43c5d6 100644
--- a/doc/pub/week35/html/week35-reveal.html
+++ b/doc/pub/week35/html/week35-reveal.html
@@ -184,7 +184,7 @@ MathJax.Hub.Config({
-Aug 28, 2022
+Aug 29, 2022
@@ -4080,6 +4080,39 @@ $$
and finally find the second derivative of this function with respect to the vector \( \boldsymbol{s} \).
+Hint: In these exercises it is always useful to write out with summation indices the various quantities.
+As an example, consider the function
+
+
+
+$$
+f(\boldsymbol{x}) =\boldsymbol{A}\boldsymbol{x},
+$$
+
+
+
which reads for a specific component \( f_i \) (we define the matrix \( \boldsymbol{A} \) to have dimension \( n\times n \) and the vector $\boldsymbol{x} to have length \( n \))
+
+
+$$
+f_i =\sum_{j=0}^{n-1}a_{ij}x_j,
+$$
+
+
+
which leads to
+
+$$
+\frac{\partial f_i}{\partial x_j}= a_{ij},
+$$
+
+
+
and written out in terms of the vector \( \boldsymbol{x} \) we have
+
+$$
+\frac{\partial f(\boldsymbol{x})}{\partial \boldsymbol{x}}= \boldsymbol{A}.
+$$
+
+
+
diff --git a/doc/pub/week35/html/week35-solarized.html b/doc/pub/week35/html/week35-solarized.html
index 2355294cf..8373962c0 100644
--- a/doc/pub/week35/html/week35-solarized.html
+++ b/doc/pub/week35/html/week35-solarized.html
@@ -330,7 +330,7 @@ MathJax.Hub.Config({
-Aug 28, 2022
+Aug 29, 2022
@@ -3893,6 +3893,31 @@ $$
and finally find the second derivative of this function with respect to the vector \( \boldsymbol{s} \).
+Hint: In these exercises it is always useful to write out with summation indices the various quantities.
+As an example, consider the function
+
+
+$$
+f(\boldsymbol{x}) =\boldsymbol{A}\boldsymbol{x},
+$$
+
+which reads for a specific component \( f_i \) (we define the matrix \( \boldsymbol{A} \) to have dimension \( n\times n \) and the vector $\boldsymbol{x} to have length \( n \))
+
+$$
+f_i =\sum_{j=0}^{n-1}a_{ij}x_j,
+$$
+
+which leads to
+$$
+\frac{\partial f_i}{\partial x_j}= a_{ij},
+$$
+
+and written out in terms of the vector \( \boldsymbol{x} \) we have
+$$
+\frac{\partial f(\boldsymbol{x})}{\partial \boldsymbol{x}}= \boldsymbol{A}.
+$$
+
+
diff --git a/doc/pub/week35/html/week35.html b/doc/pub/week35/html/week35.html
index c3d9f8c2b..dd23adbae 100644
--- a/doc/pub/week35/html/week35.html
+++ b/doc/pub/week35/html/week35.html
@@ -407,7 +407,7 @@ MathJax.Hub.Config({
-Aug 28, 2022
+Aug 29, 2022
@@ -3970,6 +3970,31 @@ $$
and finally find the second derivative of this function with respect to the vector \( \boldsymbol{s} \).
+Hint: In these exercises it is always useful to write out with summation indices the various quantities.
+As an example, consider the function
+
+
+$$
+f(\boldsymbol{x}) =\boldsymbol{A}\boldsymbol{x},
+$$
+
+which reads for a specific component \( f_i \) (we define the matrix \( \boldsymbol{A} \) to have dimension \( n\times n \) and the vector $\boldsymbol{x} to have length \( n \))
+
+$$
+f_i =\sum_{j=0}^{n-1}a_{ij}x_j,
+$$
+
+which leads to
+$$
+\frac{\partial f_i}{\partial x_j}= a_{ij},
+$$
+
+and written out in terms of the vector \( \boldsymbol{x} \) we have
+$$
+\frac{\partial f(\boldsymbol{x})}{\partial \boldsymbol{x}}= \boldsymbol{A}.
+$$
+
+
diff --git a/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz b/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz
index a750b3092..84261de1f 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 f085e51ea..5ab096820 100644
--- a/doc/pub/week35/ipynb/week35.ipynb
+++ b/doc/pub/week35/ipynb/week35.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "3e45668b",
+ "id": "857ebf60",
"metadata": {
"editable": true
},
@@ -14,7 +14,7 @@
},
{
"cell_type": "markdown",
- "id": "96c2a9a7",
+ "id": "7c69e765",
"metadata": {
"editable": true
},
@@ -22,14 +22,14 @@
"# Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression\n",
"**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
"\n",
- "Date: **Aug 28, 2022**\n",
+ "Date: **Aug 29, 2022**\n",
"\n",
"Copyright 1999-2022, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license"
]
},
{
"cell_type": "markdown",
- "id": "b9b1dee3",
+ "id": "70b6e8c3",
"metadata": {
"editable": true
},
@@ -45,7 +45,7 @@
},
{
"cell_type": "markdown",
- "id": "196a7b50",
+ "id": "18281f62",
"metadata": {
"editable": true
},
@@ -65,7 +65,7 @@
},
{
"cell_type": "markdown",
- "id": "fa347722",
+ "id": "71a7a8a0",
"metadata": {
"editable": true
},
@@ -86,7 +86,7 @@
},
{
"cell_type": "markdown",
- "id": "1df41216",
+ "id": "e8e30c07",
"metadata": {
"editable": true
},
@@ -120,7 +120,7 @@
},
{
"cell_type": "markdown",
- "id": "2eba12b1",
+ "id": "fd57437f",
"metadata": {
"editable": true
},
@@ -142,7 +142,7 @@
},
{
"cell_type": "markdown",
- "id": "6aeed722",
+ "id": "1de27555",
"metadata": {
"editable": true
},
@@ -170,7 +170,7 @@
},
{
"cell_type": "markdown",
- "id": "f74824ae",
+ "id": "9f79d654",
"metadata": {
"editable": true
},
@@ -185,7 +185,7 @@
},
{
"cell_type": "markdown",
- "id": "d60c8f15",
+ "id": "c855f536",
"metadata": {
"editable": true
},
@@ -197,7 +197,7 @@
},
{
"cell_type": "markdown",
- "id": "117e4f21",
+ "id": "190fac2f",
"metadata": {
"editable": true
},
@@ -212,7 +212,7 @@
},
{
"cell_type": "markdown",
- "id": "4d88b9ae",
+ "id": "2b13ae84",
"metadata": {
"editable": true
},
@@ -225,7 +225,7 @@
},
{
"cell_type": "markdown",
- "id": "e65f25d3",
+ "id": "229fad89",
"metadata": {
"editable": true
},
@@ -237,7 +237,7 @@
},
{
"cell_type": "markdown",
- "id": "4e2ec2e2",
+ "id": "0b0a87d1",
"metadata": {
"editable": true
},
@@ -247,7 +247,7 @@
},
{
"cell_type": "markdown",
- "id": "a6400b51",
+ "id": "a3e083d8",
"metadata": {
"editable": true
},
@@ -258,7 +258,7 @@
},
{
"cell_type": "markdown",
- "id": "f3885eea",
+ "id": "7bd61355",
"metadata": {
"editable": true
},
@@ -276,7 +276,7 @@
},
{
"cell_type": "markdown",
- "id": "5376438f",
+ "id": "ce39752f",
"metadata": {
"editable": true
},
@@ -287,7 +287,7 @@
},
{
"cell_type": "markdown",
- "id": "f0bcd883",
+ "id": "8b3484eb",
"metadata": {
"editable": true
},
@@ -299,7 +299,7 @@
},
{
"cell_type": "markdown",
- "id": "110ff751",
+ "id": "aaa377a5",
"metadata": {
"editable": true
},
@@ -309,7 +309,7 @@
},
{
"cell_type": "markdown",
- "id": "57351b69",
+ "id": "0d6cc89f",
"metadata": {
"editable": true
},
@@ -321,7 +321,7 @@
},
{
"cell_type": "markdown",
- "id": "c0ecb3e7",
+ "id": "7f035f76",
"metadata": {
"editable": true
},
@@ -331,7 +331,7 @@
},
{
"cell_type": "markdown",
- "id": "02cf22e5",
+ "id": "eef509b8",
"metadata": {
"editable": true
},
@@ -343,7 +343,7 @@
},
{
"cell_type": "markdown",
- "id": "ea5aa13f",
+ "id": "e068339c",
"metadata": {
"editable": true
},
@@ -353,7 +353,7 @@
},
{
"cell_type": "markdown",
- "id": "8446d4b9",
+ "id": "f17203b9",
"metadata": {
"editable": true
},
@@ -372,7 +372,7 @@
},
{
"cell_type": "markdown",
- "id": "16f16bec",
+ "id": "86c0c5af",
"metadata": {
"editable": true
},
@@ -382,7 +382,7 @@
},
{
"cell_type": "markdown",
- "id": "f57ce2ea",
+ "id": "63cdac3e",
"metadata": {
"editable": true
},
@@ -394,7 +394,7 @@
},
{
"cell_type": "markdown",
- "id": "5b858470",
+ "id": "5abe0dc3",
"metadata": {
"editable": true
},
@@ -404,7 +404,7 @@
},
{
"cell_type": "markdown",
- "id": "1447bafa",
+ "id": "0f30d114",
"metadata": {
"editable": true
},
@@ -420,7 +420,7 @@
},
{
"cell_type": "markdown",
- "id": "b9904eda",
+ "id": "0ea9ba9f",
"metadata": {
"editable": true
},
@@ -440,7 +440,7 @@
},
{
"cell_type": "markdown",
- "id": "27355bfb",
+ "id": "30cb0f64",
"metadata": {
"editable": true
},
@@ -450,7 +450,7 @@
},
{
"cell_type": "markdown",
- "id": "a559bb95",
+ "id": "e5ed503a",
"metadata": {
"editable": true
},
@@ -461,7 +461,7 @@
},
{
"cell_type": "markdown",
- "id": "5c73ce5a",
+ "id": "2060d4e4",
"metadata": {
"editable": true
},
@@ -480,7 +480,7 @@
},
{
"cell_type": "markdown",
- "id": "c19759b8",
+ "id": "b0fd7136",
"metadata": {
"editable": true
},
@@ -490,7 +490,7 @@
},
{
"cell_type": "markdown",
- "id": "ac0857a5",
+ "id": "637567c7",
"metadata": {
"editable": true
},
@@ -502,7 +502,7 @@
},
{
"cell_type": "markdown",
- "id": "e69bfd6b",
+ "id": "af22a079",
"metadata": {
"editable": true
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@@ -512,7 +512,7 @@
},
{
"cell_type": "markdown",
- "id": "9b9025d3",
+ "id": "2ee152dc",
"metadata": {
"editable": true
},
@@ -523,7 +523,7 @@
},
{
"cell_type": "markdown",
- "id": "e9021e46",
+ "id": "8d04574d",
"metadata": {
"editable": true
},
@@ -543,7 +543,7 @@
},
{
"cell_type": "markdown",
- "id": "6060ea13",
+ "id": "da61cd14",
"metadata": {
"editable": true
},
@@ -555,7 +555,7 @@
},
{
"cell_type": "markdown",
- "id": "f526f7d2",
+ "id": "c716c45d",
"metadata": {
"editable": true
},
@@ -570,7 +570,7 @@
{
"cell_type": "code",
"execution_count": 1,
- "id": "470a8637",
+ "id": "5033a6c0",
"metadata": {
"collapsed": false,
"editable": true
@@ -652,7 +652,7 @@
},
{
"cell_type": "markdown",
- "id": "72fa9405",
+ "id": "c9637b20",
"metadata": {
"editable": true
},
@@ -662,7 +662,7 @@
},
{
"cell_type": "markdown",
- "id": "ef0e913e",
+ "id": "89d9e3ca",
"metadata": {
"editable": true
},
@@ -674,7 +674,7 @@
},
{
"cell_type": "markdown",
- "id": "f7058dfe",
+ "id": "a02bfbc1",
"metadata": {
"editable": true
},
@@ -684,7 +684,7 @@
},
{
"cell_type": "markdown",
- "id": "986ff34a",
+ "id": "ede8fe00",
"metadata": {
"editable": true
},
@@ -695,7 +695,7 @@
},
{
"cell_type": "markdown",
- "id": "0004714a",
+ "id": "5ede9382",
"metadata": {
"editable": true
},
@@ -707,7 +707,7 @@
},
{
"cell_type": "markdown",
- "id": "510ee51f",
+ "id": "5a996440",
"metadata": {
"editable": true
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@@ -717,7 +717,7 @@
},
{
"cell_type": "markdown",
- "id": "97103ec0",
+ "id": "a79ce454",
"metadata": {
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@@ -729,7 +729,7 @@
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{
"cell_type": "markdown",
- "id": "9ee6533e",
+ "id": "0280764d",
"metadata": {
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@@ -739,7 +739,7 @@
},
{
"cell_type": "markdown",
- "id": "07ca221a",
+ "id": "c94f63a0",
"metadata": {
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@@ -751,7 +751,7 @@
},
{
"cell_type": "markdown",
- "id": "25107b36",
+ "id": "04b1d08c",
"metadata": {
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@@ -764,7 +764,7 @@
},
{
"cell_type": "markdown",
- "id": "bd79ed8d",
+ "id": "be384767",
"metadata": {
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@@ -776,7 +776,7 @@
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{
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+ "id": "13b6ce20",
"metadata": {
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@@ -786,7 +786,7 @@
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{
"cell_type": "markdown",
- "id": "66a153ce",
+ "id": "82bef906",
"metadata": {
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@@ -798,7 +798,7 @@
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{
"cell_type": "markdown",
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+ "id": "82e72e60",
"metadata": {
"editable": true
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@@ -810,7 +810,7 @@
},
{
"cell_type": "markdown",
- "id": "79dc1590",
+ "id": "39fc1d21",
"metadata": {
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},
@@ -821,7 +821,7 @@
},
{
"cell_type": "markdown",
- "id": "21c71a8d",
+ "id": "4876d43d",
"metadata": {
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@@ -833,7 +833,7 @@
},
{
"cell_type": "markdown",
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+ "id": "0bc0fa1a",
"metadata": {
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@@ -852,7 +852,7 @@
},
{
"cell_type": "markdown",
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+ "id": "5124b2d5",
"metadata": {
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@@ -865,7 +865,7 @@
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{
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@@ -875,7 +875,7 @@
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{
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+ "id": "761a1f2d",
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@@ -887,7 +887,7 @@
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{
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@@ -897,7 +897,7 @@
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{
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@@ -909,7 +909,7 @@
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{
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@@ -919,7 +919,7 @@
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{
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@@ -931,7 +931,7 @@
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{
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@@ -942,7 +942,7 @@
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{
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@@ -954,7 +954,7 @@
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@@ -1096,7 +1096,7 @@
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@@ -1108,7 +1108,7 @@
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@@ -1148,7 +1148,7 @@
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@@ -1159,7 +1159,7 @@
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@@ -1193,7 +1193,7 @@
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@@ -1961,7 +1961,7 @@
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@@ -1981,7 +1981,7 @@
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@@ -2008,7 +2008,7 @@
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@@ -2033,7 +2033,7 @@
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@@ -2119,7 +2119,7 @@
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@@ -2442,7 +2442,7 @@
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@@ -2511,7 +2511,7 @@
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@@ -2923,7 +2923,7 @@
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@@ -4503,7 +4503,7 @@
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@@ -4529,7 +4529,7 @@
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@@ -4590,7 +4590,7 @@
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@@ -4602,7 +4602,7 @@
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@@ -4624,7 +4624,7 @@
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@@ -4636,7 +4636,7 @@
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@@ -4658,7 +4658,7 @@
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@@ -4668,7 +4668,7 @@
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@@ -4680,7 +4680,7 @@
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@@ -4697,7 +4697,7 @@
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@@ -4710,7 +4710,7 @@
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@@ -4722,7 +4722,7 @@
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@@ -4732,7 +4732,7 @@
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@@ -4745,7 +4745,7 @@
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@@ -4755,7 +4755,7 @@
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@@ -4780,7 +4780,7 @@
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@@ -4793,7 +4793,7 @@
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@@ -4805,7 +4805,7 @@
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@@ -4852,7 +4852,7 @@
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@@ -4864,7 +4864,7 @@
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@@ -4876,7 +4876,7 @@
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@@ -4888,7 +4888,7 @@
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@@ -4936,7 +4936,7 @@
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@@ -4948,7 +4948,7 @@
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@@ -4960,7 +4960,7 @@
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@@ -4972,7 +4972,7 @@
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@@ -4984,7 +4984,7 @@
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@@ -5003,7 +5003,7 @@
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@@ -5025,7 +5025,7 @@
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@@ -5047,7 +5047,7 @@
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@@ -5059,7 +5059,7 @@
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@@ -5071,7 +5071,7 @@
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@@ -5087,7 +5087,7 @@
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+ "id": "13a365db",
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@@ -5099,7 +5099,7 @@
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@@ -5111,7 +5111,7 @@
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{
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+ "id": "f2e58fd5",
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@@ -5121,7 +5121,7 @@
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{
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+ "id": "16de869f",
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@@ -5133,7 +5133,7 @@
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{
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@@ -5143,7 +5143,7 @@
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@@ -5155,7 +5155,7 @@
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@@ -5172,7 +5172,7 @@
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+ "id": "9b9baa8c",
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@@ -5184,7 +5184,7 @@
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@@ -5196,7 +5196,7 @@
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@@ -5206,7 +5206,7 @@
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@@ -5218,7 +5218,7 @@
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@@ -5228,7 +5228,7 @@
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@@ -5240,7 +5240,7 @@
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@@ -5250,7 +5250,7 @@
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@@ -5262,7 +5262,7 @@
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@@ -5272,7 +5272,7 @@
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@@ -5284,7 +5284,7 @@
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@@ -5353,7 +5353,7 @@
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{
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@@ -5367,7 +5367,7 @@
{
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- "id": "07a79ed1",
+ "id": "11d52f8e",
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@@ -5380,7 +5380,7 @@
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{
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+ "id": "484e9a34",
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@@ -5394,7 +5394,7 @@
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{
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+ "id": "b0cdfb10",
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@@ -5407,7 +5407,7 @@
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@@ -5418,7 +5418,7 @@
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{
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+ "id": "861d3d39",
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@@ -5430,7 +5430,7 @@
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{
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+ "id": "3b328966",
"metadata": {
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@@ -5440,7 +5440,7 @@
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{
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- "id": "ef8754ad",
+ "id": "2ce8a476",
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@@ -5452,7 +5452,7 @@
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{
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+ "id": "24f4119e",
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@@ -5468,7 +5468,7 @@
{
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- "id": "f6ccb6f3",
+ "id": "10eaa5b1",
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@@ -5519,7 +5519,7 @@
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{
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+ "id": "fa18a2c3",
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@@ -5529,7 +5529,7 @@
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{
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+ "id": "3eab6da8",
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@@ -5575,7 +5575,7 @@
{
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- "id": "80c09d31",
+ "id": "7c79afc0",
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@@ -5588,7 +5588,7 @@
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{
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- "id": "def42471",
+ "id": "f27a8670",
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@@ -5599,7 +5599,7 @@
{
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- "id": "4d5139dd",
+ "id": "d44a1971",
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@@ -5614,7 +5614,7 @@
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{
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- "id": "018b50ac",
+ "id": "e52c7041",
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@@ -5632,7 +5632,7 @@
{
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- "id": "1edd528d",
+ "id": "b2615852",
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@@ -5649,7 +5649,7 @@
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{
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- "id": "77169222",
+ "id": "5a287475",
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@@ -5659,7 +5659,7 @@
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{
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+ "id": "5ff6ac25",
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@@ -5670,7 +5670,7 @@
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+ "id": "1f3ecf4e",
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@@ -5681,7 +5681,7 @@
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{
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+ "id": "b0b36a14",
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@@ -5692,7 +5692,7 @@
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{
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- "id": "3dcde514",
+ "id": "fec5b373",
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@@ -5715,7 +5715,7 @@
{
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- "id": "7452c257",
+ "id": "44758072",
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@@ -5728,7 +5728,7 @@
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- "id": "11b072a0",
+ "id": "08b494d0",
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@@ -5743,7 +5743,7 @@
{
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- "id": "2cdafc75",
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@@ -5823,7 +5823,7 @@
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{
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@@ -5838,7 +5838,7 @@
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{
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@@ -5851,7 +5851,7 @@
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{
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+ "id": "b710d956",
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@@ -5862,7 +5862,7 @@
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{
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- "id": "c2918ec5",
+ "id": "710d2390",
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@@ -5874,7 +5874,7 @@
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{
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+ "id": "4df4e71e",
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@@ -5884,7 +5884,7 @@
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{
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- "id": "b732a702",
+ "id": "fb0bddac",
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@@ -5896,7 +5896,7 @@
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{
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- "id": "7c0b94e1",
+ "id": "a32a38fd",
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@@ -5906,7 +5906,7 @@
},
{
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- "id": "9bcdb98e",
+ "id": "6274f8a3",
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@@ -5928,7 +5928,7 @@
},
{
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- "id": "f81f9ea6",
+ "id": "80db0e71",
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@@ -5940,7 +5940,7 @@
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{
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- "id": "981d64f2",
+ "id": "80b9429b",
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@@ -5950,7 +5950,7 @@
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{
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- "id": "ac2ee398",
+ "id": "2e227f6e",
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@@ -5962,7 +5962,7 @@
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{
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- "id": "6105a22e",
+ "id": "ddfbccf9",
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@@ -5972,7 +5972,7 @@
},
{
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- "id": "c26a78ab",
+ "id": "2aa4901e",
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@@ -5984,12 +5984,93 @@
},
{
"cell_type": "markdown",
- "id": "56b85f17",
+ "id": "1cb6ca43",
"metadata": {
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},
"source": [
- "and finally find the second derivative of this function with respect to the vector $\\boldsymbol{s}$."
+ "and finally find the second derivative of this function with respect to the vector $\\boldsymbol{s}$.\n",
+ "\n",
+ "**Hint**: In these exercises it is always useful to write out with summation indices the various quantities.\n",
+ "As an example, consider the function"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "029cdf55",
+ "metadata": {
+ "editable": true
+ },
+ "source": [
+ "$$\n",
+ "f(\\boldsymbol{x}) =\\boldsymbol{A}\\boldsymbol{x},\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "783a6515",
+ "metadata": {
+ "editable": true
+ },
+ "source": [
+ "which reads for a specific component $f_i$ (we define the matrix $\\boldsymbol{A}$ to have dimension $n\\times n$ and the vector $\\boldsymbol{x} to have length $n$)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "41c6d04e",
+ "metadata": {
+ "editable": true
+ },
+ "source": [
+ "$$\n",
+ "f_i =\\sum_{j=0}^{n-1}a_{ij}x_j,\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "24481dd4",
+ "metadata": {
+ "editable": true
+ },
+ "source": [
+ "which leads to"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "49b7aa71",
+ "metadata": {
+ "editable": true
+ },
+ "source": [
+ "$$\n",
+ "\\frac{\\partial f_i}{\\partial x_j}= a_{ij},\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6900d4ad",
+ "metadata": {
+ "editable": true
+ },
+ "source": [
+ "and written out in terms of the vector $\\boldsymbol{x}$ we have"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "50e6bb13",
+ "metadata": {
+ "editable": true
+ },
+ "source": [
+ "$$\n",
+ "\\frac{\\partial f(\\boldsymbol{x})}{\\partial \\boldsymbol{x}}= \\boldsymbol{A}.\n",
+ "$$"
]
}
],
diff --git a/doc/src/week35/week35.do.txt b/doc/src/week35/week35.do.txt
index e70c02bec..9d6903cfe 100644
--- a/doc/src/week35/week35.do.txt
+++ b/doc/src/week35/week35.do.txt
@@ -2921,3 +2921,31 @@ and
\]
!et
and finally find the second derivative of this function with respect to the vector $\bm{s}$.
+
+_Hint_: In these exercises it is always useful to write out with summation indices the various quantities.
+As an example, consider the function
+
+!bt
+\[
+f(\bm{x}) =\bm{A}\bm{x},
+\]
+!et
+which reads for a specific component $f_i$ (we define the matrix $\bm{A}$ to have dimension $n\times n$ and the vector $\bm{x} to have length $n$)
+
+!bt
+\[
+f_i =\sum_{j=0}^{n-1}a_{ij}x_j,
+\]
+!et
+which leads to
+!bt
+\[
+\frac{\partial f_i}{\partial x_j}= a_{ij},
+\]
+!et
+and written out in terms of the vector $\bm{x}$ we have
+!bt
+\[
+\frac{\partial f(\bm{x})}{\partial \bm{x}}= \bm{A}.
+\]
+!et