Question

Why is $\triangledown_x x^TA^TAx = 2A^TAx$ not $2x^TA^TA$?

score 955 · Answer 1 · 2018-10-16 00:01:59

955

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Why is $\triangledown_x x^TA^TAx = 2A^TAx$ not $2x^TA^TA$?

Published on 16 Oct 2018 - 0:01

score 314 · Answer 2 · 2026-03-26 03:13:27

314

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Write the derivative of the lower-triangular matrix $L(t)$ in terms of $L(t)$, $L^{-1}(t)$ and $\frac{d}{dt}A(t)$, where $A(t)=L(t)L^T(t)$

Published on 26 Mar 2026 - 3:13

score 37 · Answer 3 · 2026-03-26 04:51:56

37

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What can I say about $\mathbf{X}$ if $\mathbf{y}^{\mathrm{T}} \mathbf{X} \mathbf{y} = \mathbf{z}^{\mathrm{T}} \mathbf{X} \mathbf{z}$?

Published on 26 Mar 2026 - 4:51

score 117 · Answer 4 · 2018-10-17 14:34:47

117

Views

Matrix functions reducing eigenspectrum degeneracy?

Published on 17 Oct 2018 - 14:34

score 1.3k · Answer 5 · 2026-03-24 23:44:58

1.3k

Views

Gradient of $X \mapsto \mbox{trace} \left( X^T A X \right)$

Published on 24 Mar 2026 - 23:44

score 1.6k · Answer 6 · 2026-03-25 06:09:52

1.6k

Views

matrix block multiplication definition, properties and applications

Published on 25 Mar 2026 - 6:09

score 276 · Answer 7 · 2018-10-19 15:44:07

276

Views

Gradient of the Lie exponential map on SO(n)

Published on 19 Oct 2018 - 15:44

score 914 · Answer 8 · 2018-10-20 02:33:02

914

Views

Gradient of a complex valued matrix function but with real domain

Published on 20 Oct 2018 - 2:33

score 34 · Answer 9 · 2018-10-20 02:36:00

34

Views

How does one derive with respect to a matrix when that matrix is part of a summation whose result is inverted?

Published on 20 Oct 2018 - 2:36

score 138 · Answer 10 · 2018-10-21 19:37:51

138

Views

Gradient of a Scalar Function of a Matrix

Published on 21 Oct 2018 - 19:37

score 110 · Answer 11 · 2026-03-26 04:31:39

110

Views

Is the solution to $A-O(A)=\tilde \Sigma$ unique?

Published on 26 Mar 2026 - 4:31

score 2.3k · Answer 12 · 2018-10-23 17:25:54

2.3k

Views

Proof of the derivative of a quadratic form

Published on 23 Oct 2018 - 17:25

score 92 · Answer 13 · 2026-03-26 06:10:54

92

Views

How can I calculate the gradient of the product of a matrix and a vector?

Published on 26 Mar 2026 - 6:10

score 100 · Answer 14 · 2018-10-24 14:49:59

100

Views

How to optimize $ f(X)= \| X-M||_F^2 \\ $ with constraint $\sigma_{k+1}(X) \le a $

Published on 24 Oct 2018 - 14:49

score 79 · Answer 15 · 2018-10-24 16:11:18

79

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How to take derivative of Ky Fan $k$ norms of a matrix $A$: $\frac{\partial\|A\|_k}{\partial A}$

Published on 24 Oct 2018 - 16:11

List Question

Why is $\triangledown_x x^TA^TAx = 2A^TAx$ not $2x^TA^TA$?

Write the derivative of the lower-triangular matrix $L(t)$ in terms of $L(t)$, $L^{-1}(t)$ and $\frac{d}{dt}A(t)$, where $A(t)=L(t)L^T(t)$

What can I say about $\mathbf{X}$ if $\mathbf{y}^{\mathrm{T}} \mathbf{X} \mathbf{y} = \mathbf{z}^{\mathrm{T}} \mathbf{X} \mathbf{z}$?

Matrix functions reducing eigenspectrum degeneracy?

Gradient of $X \mapsto \mbox{trace} \left( X^T A X \right)$

matrix block multiplication definition, properties and applications

Gradient of the Lie exponential map on SO(n)

Gradient of a complex valued matrix function but with real domain

How does one derive with respect to a matrix when that matrix is part of a summation whose result is inverted?

Gradient of a Scalar Function of a Matrix

Is the solution to $A-O(A)=\tilde \Sigma$ unique?

Proof of the derivative of a quadratic form

How can I calculate the gradient of the product of a matrix and a vector?

How to optimize $ f(X)= \| X-M||_F^2 \\ $ with constraint $\sigma_{k+1}(X) \le a $

How to take derivative of Ky Fan $k$ norms of a matrix $A$: $\frac{\partial\|A\|_k}{\partial A}$

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