List questions from matrix-calculus

Published on 14 Apr 2026 - 11:06

151

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Prove $ \mbox{adj} (A) = \left[ \frac{\partial }{\partial a_{ij} } \det(A) \right]^T $

Published on 14 Apr 2026 - 22:48

89

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Generalizing an eigenvalue decomposition

Published on 13 Apr 2026 - 15:00

61

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Can I show a matrix equation has a unique minima by showing it is convex?

Published on 11 Apr 2026 - 19:31

52

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What is this condition?

Published on 14 Apr 2026 - 20:47

75

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Idea how to solve linear equation for linearly dependent columns

Published on 08 Apr 2026 - 21:42

59

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Derivate of powers of stochastic matricies with respect to its elements

Published on 12 Apr 2026 - 22:58

148

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Product of square matrices

Published on 15 Apr 2026 - 7:37

514

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First-order Taylor approximation of matrix function

Published on 12 Apr 2026 - 14:33

2k

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The matrix logarithm is well-defined - but how can we algebraically see that it is inverse to the exponential, as a finite polynomial?

Published on 13 Apr 2026 - 1:45

86

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Simple Matrix inequality

Published on 14 Apr 2026 - 15:57

330

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Derive the derivative of cost function of logistic regression.

Published on 12 Apr 2026 - 23:12

28

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$\partial_{\mu} \exp[X] = \int_{0}^{1} d \alpha \exp[\alpha X] \partial_{\mu}{X} \exp[(1-\alpha)X]$

Published on 15 Apr 2026 - 21:49

116

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Derivative of $X \mapsto \frac{AXA}{\operatorname{Tr} \left( AXA \right )}$

Published on 16 Apr 2026 - 13:32

154

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Second derivative of a matrix function

Published on 14 Apr 2026 - 21:17

List Question

Can all 4-order tensors represented by a matrix?

Prove $ \mbox{adj} (A) = \left[ \frac{\partial }{\partial a_{ij} } \det(A) \right]^T $

Generalizing an eigenvalue decomposition

Can I show a matrix equation has a unique minima by showing it is convex?

What is this condition?

Idea how to solve linear equation for linearly dependent columns

Derivate of powers of stochastic matricies with respect to its elements

Product of square matrices

First-order Taylor approximation of matrix function

The matrix logarithm is well-defined - but how can we algebraically see that it is inverse to the exponential, as a finite polynomial?

Simple Matrix inequality

Derive the derivative of cost function of logistic regression.

$\partial_{\mu} \exp[X] = \int_{0}^{1} d \alpha \exp[\alpha X] \partial_{\mu}{X} \exp[(1-\alpha)X]$

Derivative of $X \mapsto \frac{AXA}{\operatorname{Tr} \left( AXA \right )}$

Second derivative of a matrix function

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