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, where tr(X) is the trace of the matrix X. Equivalently, if dA stands for the differential of A, the formula is It is named after the mathematician C.G.J. Jacobi.

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, where tr(X) is the trace of the matrix X. Equivalently, if dA stands for the differential of A, the formula is It is named after the mathematician C.G.J. Jacobi.