List questions from scalar-fields

Published on 16 Mar 2017 - 10:10

229

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Scalar line integrals vs. line integrals when to calculate each?

Published on 18 Mar 2017 - 17:40

32

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Some insight about the directional derivative

Published on 22 Mar 2017 - 20:24

117

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Vector Field Verification

Published on 28 Mar 2017 - 10:23

826

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Is every vector field the gradient of a scalar field?

Published on 08 Apr 2017 - 15:09

104

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Why is function $X \mapsto z^T X z$ linear?

Published on 28 Feb 2023 - 7:35

191

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Gradient of $X \mapsto \mbox{tr} \left(BXCX^TB^TBXCX^TB^T\right)$

Published on 04 Mar 2023 - 5:20

96

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Show $\nabla f=A\nabla g$ by chain rule

Published on 07 Mar 2023 - 1:56

92

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Stuck while differentiating $x\mapsto\|x\|^2 + \lambda{\|Ax - b\|}^2$

Published on 29 Mar 2023 - 13:04

131

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Derivative of $\varphi({\bf X}) = \sum_{i=1}^n \lambda_i({\bf X}) \log \lambda_i({\bf X})$

Published on 30 Mar 2023 - 8:17

83

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How do you find the scalar field of the vector field $F=-y\hat{i}+x\hat{j}$

Published on 12 Apr 2023 - 15:01

77

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Gradient of a function w.r.t. matrices

Published on 15 Apr 2023 - 10:30

194

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Gradient of $C \mapsto\frac{1}{2}\left\lVert CA - BC \right\rVert_F^2$

Published on 25 Apr 2023 - 9:13

51

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Is the gradient of a function $f : \mathbb{R}^2 \to \mathbb{R}^1$ the best $1$-dimensional approximated linear transformation at a point $v$?

Published on 04 May 2023 - 15:17

143

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Mean-value theorem for function of matrices

Published on 23 Feb 2026 - 16:38

List Question

Gradient of $a^T X b$ with respect to $X$

Scalar line integrals vs. line integrals when to calculate each?

Some insight about the directional derivative

Vector Field Verification

Is every vector field the gradient of a scalar field?

Why is function $X \mapsto z^T X z$ linear?

Gradient of $X \mapsto \mbox{tr} \left(BXCX^TB^TBXCX^TB^T\right)$

Show $\nabla f=A\nabla g$ by chain rule

Stuck while differentiating $x\mapsto\|x\|^2 + \lambda{\|Ax - b\|}^2$

Derivative of $\varphi({\bf X}) = \sum_{i=1}^n \lambda_i({\bf X}) \log \lambda_i({\bf X})$

How do you find the scalar field of the vector field $F=-y\hat{i}+x\hat{j}$

Gradient of a function w.r.t. matrices

Gradient of $C \mapsto\frac{1}{2}\left\lVert CA - BC \right\rVert_F^2$

Is the gradient of a function $f : \mathbb{R}^2 \to \mathbb{R}^1$ the best $1$-dimensional approximated linear transformation at a point $v$?

Mean-value theorem for function of matrices

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