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Jacobi's formula
Formula for the derivative of a matrix determinant
Jacobi's formula
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...
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