From f1951cb28a78af62593f9ba61a2d9925efb8edff Mon Sep 17 00:00:00 2001 From: Morten Hjorth-Jensen Date: Sun, 27 Aug 2023 10:09:23 +0200 Subject: [PATCH] Update week35.do.txt --- doc/src/week35/week35.do.txt | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/doc/src/week35/week35.do.txt b/doc/src/week35/week35.do.txt index a95033659..39141762a 100644 --- a/doc/src/week35/week35.do.txt +++ b/doc/src/week35/week35.do.txt @@ -536,6 +536,11 @@ on the other hand $\bm{y}$ is a scalar, the Jacobian becomes a $1\times n$ matrix. +When this matrix is a square matrix $m=n$, its determinant is often referred to as the Jacobian +determinant. Both the matrix and (if $m=n$) the determinant are +often referred to simply as the Jacobian. The Jacobian matrix represents the differential of $\bm{y}$ at every point where the +vector is differentiable. + !split ===== Derivatives, example 1 ===== @@ -562,6 +567,8 @@ From this we have, using the definition of the Jacobian \] !et +!split +===== Example 2 =====