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Applications of matrix differentiation

score 330 · Answer 1 · 2026-04-10 18:21:32

330

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Applications of matrix differentiation

Published on 10 Apr 2026 - 18:21

score 83 · Answer 2 · 2026-04-16 13:41:42

83

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matrix calculus: derivative of $\frac{x^T r}{\sqrt{x^T Sx}}$ with respect to $x$

Published on 16 Apr 2026 - 13:41

score 85 · Answer 3 · 2026-04-16 02:10:16

85

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$x,y$ are vectors and $\Lambda$ is a symmetric square matrix, $y = \frac{x}{\sqrt{x^T \Lambda x}}$ solve for vector $x$

Published on 16 Apr 2026 - 2:10

score 43 · Answer 4 · 2026-04-16 17:34:43

43

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The Scalar-to-Matrix Derivative of $\frac 1 2 \| \vec{1}^T \sigma \left( W X \right) - \sigma \left( e_1^T X \right) \|_F^2$ w.r.t $W$

Published on 16 Apr 2026 - 17:34

score 107 · Answer 5 · 2026-04-12 01:55:32

107

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Backward propagation math: where does -1 come from?

Published on 12 Apr 2026 - 1:55

score 98 · Answer 6 · 2026-04-09 17:12:57

98

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When is $AA^T$ a strictly positive definite matrix?

Published on 09 Apr 2026 - 17:12

score 93 · Answer 7 · 2026-04-11 13:27:51

93

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Are the inverse of "nearly" diagonal nonsingular matrices also "nearly" diagonal?

Published on 11 Apr 2026 - 13:27

score 241 · Answer 8 · 2026-04-14 04:22:29

241

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Partial derivatives using Einstein / Index notation

Published on 14 Apr 2026 - 4:22

score 146 · Answer 9 · 2026-04-12 10:52:48

146

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Jacobi Formula for determinants misconception?

Published on 12 Apr 2026 - 10:52

score 1.5k · Answer 10 · 2026-04-14 07:02:09

1.5k

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Why is the derivative of the identity matrix 0?

Published on 14 Apr 2026 - 7:02

score 67 · Answer 11 · 2026-04-16 02:08:54

67

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Matrix Taylor series and differentiation: how do we show that if $X=A-tB$, $\frac{d^j}{dt^j}X^{-1}=(-1)^jj!X^{-1}(X'X^{-1})^j$?

Published on 16 Apr 2026 - 2:08

score 590 · Answer 12 · 2026-04-14 17:33:06

590

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derivative of trace of (XAX) w.r.t X when X is symmetric?

Published on 14 Apr 2026 - 17:33

score 153 · Answer 13 · 2026-04-13 02:53:24

153

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Derivative of $Y \mapsto Y^T Y$

Published on 13 Apr 2026 - 2:53

score 61 · Answer 14 · 2026-04-13 16:44:09

61

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Estimation for solution of the Lyapunov equation with semidefinite right-hand side

Published on 13 Apr 2026 - 16:44

score 86 · Answer 15 · 2026-04-11 03:00:45

86

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Funky derivative of trace of matrix with composition

Published on 11 Apr 2026 - 3:00

List Question

Applications of matrix differentiation

matrix calculus: derivative of $\frac{x^T r}{\sqrt{x^T Sx}}$ with respect to $x$

$x,y$ are vectors and $\Lambda$ is a symmetric square matrix, $y = \frac{x}{\sqrt{x^T \Lambda x}}$ solve for vector $x$

The Scalar-to-Matrix Derivative of $\frac 1 2 \| \vec{1}^T \sigma \left( W X \right) - \sigma \left( e_1^T X \right) \|_F^2$ w.r.t $W$

Backward propagation math: where does -1 come from?

When is $AA^T$ a strictly positive definite matrix?

Are the inverse of "nearly" diagonal nonsingular matrices also "nearly" diagonal?

Partial derivatives using Einstein / Index notation

Jacobi Formula for determinants misconception?

Why is the derivative of the identity matrix 0?

Matrix Taylor series and differentiation: how do we show that if $X=A-tB$, $\frac{d^j}{dt^j}X^{-1}=(-1)^jj!X^{-1}(X'X^{-1})^j$?

derivative of trace of (XAX) w.r.t X when X is symmetric?

Derivative of $Y \mapsto Y^T Y$

Estimation for solution of the Lyapunov equation with semidefinite right-hand side

Funky derivative of trace of matrix with composition

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