Jacobi's formula
id:
jacobi-s-formula-165-14827670
title:
Jacobi's formula
text:
In matrix calculus, Jacobi's formula expresses the derivative of the determinant of a matrix A in terms of the adjugate of A and the derivative of A. If A is a differentiable map from the real numbers to n × n matrices, then
- d d t det A ( t ) = tr ( adj ( A ( t ) ) d A ( t ) d t ) = ( det A ( t ) ) ⋅ tr ( A ( t ) − 1 ⋅ d A ( t ) d t ) where tr(X) is the trace of the matrix X and adj ( X ) is its adjugate matrix. (The latter equality only holds if A(t) is invertible.) As a special cas
brand slug:
wiki
category slug:
encyclopedia
description:
Formula for the derivative of a matrix determinant
original url:
https://en.wikipedia.org/wiki/Jacobi%27s_formula
date created:
2005-07-31T22:41:54Z
date modified:
2024-08-29T12:33:56Z
main entity:
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image:
fields total:
13
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