List questions from scalar-fields

Published on 02 May 2022 - 12:08

106

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Calculate $\frac{\partial}{\partial \mathbf{A}}\lVert \mathbf{A}^{\top}\mathbf{AX}-\mathbf{X} \rVert _{F}^{2}$

Published on 04 May 2022 - 4:48

53

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What makes complex numbers so dominant among two-dimensional scalar fields?

Published on 05 May 2022 - 8:57

153

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Partial derivatives in scalar field taylor expansion

Published on 08 May 2022 - 10:45

173

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Surface integral of hemisphere

Published on 10 May 2022 - 17:06

41

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How to find the directional derivative at every point?

Published on 20 May 2022 - 16:06

159

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Gradient of $\mbox{tr} \left (X^T X \right)$

Published on 27 May 2022 - 0:47

15

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Remap 3D function onto a plane?

Published on 03 Mar 2026 - 21:30

31

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Parametrising Intuition of Plane

Published on 01 Jun 2022 - 13:23

51

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Differentiability of $g(x,y) := f \left(\sqrt{x^{2} + y^{2}}\right)$

Published on 13 Jun 2022 - 5:36

63

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Show that there is a point $x_0\in\Bbb{R}^n$ such that $Df(x_0)=0$

Published on 14 Jun 2022 - 18:48

57

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When is $\nabla\cdot({\bf a}\cdot{\bf r})({\bf b}\cdot{\bf r})\,{\bf F}({\bf r})=0$ for constant vectors ${\bf a}$ and ${\bf b}$?

Published on 24 Feb 2026 - 6:51

139

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What is the gradient of $x \mapsto \frac{1}{2}(x^2)^\top A(x^2)$?

Published on 08 Jul 2022 - 23:24

511

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First-order Taylor approximation of matrix function

Published on 13 Jul 2022 - 17:53

84

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If the gradient of two functions are related by a matrix can we say anything about these two functions?

Published on 17 Jul 2022 - 18:46

List Question

Find gradient and Hessian for optimization problem

Calculate $\frac{\partial}{\partial \mathbf{A}}\lVert \mathbf{A}^{\top}\mathbf{AX}-\mathbf{X} \rVert _{F}^{2}$

What makes complex numbers so dominant among two-dimensional scalar fields?

Partial derivatives in scalar field taylor expansion

Surface integral of hemisphere

How to find the directional derivative at every point?

Gradient of $\mbox{tr} \left (X^T X \right)$

Remap 3D function onto a plane?

Parametrising Intuition of Plane

Differentiability of $g(x,y) := f \left(\sqrt{x^{2} + y^{2}}\right)$

Show that there is a point $x_0\in\Bbb{R}^n$ such that $Df(x_0)=0$

When is $\nabla\cdot({\bf a}\cdot{\bf r})({\bf b}\cdot{\bf r})\,{\bf F}({\bf r})=0$ for constant vectors ${\bf a}$ and ${\bf b}$?

What is the gradient of $x \mapsto \frac{1}{2}(x^2)^\top A(x^2)$?

First-order Taylor approximation of matrix function

If the gradient of two functions are related by a matrix can we say anything about these two functions?

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