Question

Need some clarification for $\frac{d}{dt} [\det A(t)]=\det A(t) \cdot \operatorname*{tr}[A^{-1}(t)\cdot \frac{d}{dt} A(t)]$.

score 76 · Answer 1 · 2026-04-22 21:34:40

76

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Need some clarification for $\frac{d}{dt} [\det A(t)]=\det A(t) \cdot \operatorname*{tr}[A^{-1}(t)\cdot \frac{d}{dt} A(t)]$.

Published on 22 Apr 2026 - 21:34

score 82 · Answer 2 · 2026-04-13 07:17:32

82

Views

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310

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score 85 · Answer 5 · 2026-04-12 07:28:34

85

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107

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99

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37

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score 178 · Answer 13 · 2026-04-16 13:54:21

178

Views

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41

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81

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List Question

Need some clarification for $\frac{d}{dt} [\det A(t)]=\det A(t) \cdot \operatorname*{tr}[A^{-1}(t)\cdot \frac{d}{dt} A(t)]$.

Is there a way to get an approximation of $\det( \sigma_s^2A+B)^{1/N}$ in the GLRT?

Solving a third order polynomial matrix equation

Proving a unique solution with the norm of a matrix in a linear system

how det(A)=0 implies that the solution isn't unique?

Solving characteristic equation with matrix coefficients.

How to solve matrix differential equation?

Adding a constant to all elements of a matrix and solving

How should I denote vectors and matrices in equations when accessing contents within in a scientific paper?

How to calculate inverse of the special matrix $A_{(m+1)\times (m+1)}$.

What is the relationship between rank and solutions of a linear system with multiple columns?

About this simple linear system $Ax=0$ under the condition $Dim(Ker(A))>0$

How to solve the matrix equations: $\frac{1}{2}(\Omega Q - Q\Omega)=F$ for $\Omega$

Inverse matrices in an equation

Determinant of matrix with power series terms

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