List questions from scalar-fields

Published on 06 Apr 2021 - 8:32

326

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Confused about computing the gradient of least-squares cost

Published on 07 Apr 2021 - 19:40

593

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What is the gradient of $x^T A\, x$ with respect to the matrix $A$?

Published on 20 Apr 2021 - 14:22

22

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Finding Potential for specific Vector Field, help?

Published on 23 Apr 2021 - 3:08

220

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Matrix differentiation, $x^T A x$ w.r.t $A$

Published on 25 Apr 2021 - 22:59

46

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Is there a bundle concept that includes tensors and spinors as special cases?

Published on 26 Apr 2021 - 1:32

75

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Partial derivative of $x_1^TAB^Tx_2$

Published on 04 May 2021 - 7:34

278

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Prove that there exists no scalar field which has derivative $> 0$ at a fixed point wrt every direction

Published on 11 May 2021 - 14:24

290

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If $f(x) \leq f(a)$ for all $x$ in an open ball $B(a)$ , then prove that $\nabla f(a) = 0$

Published on 16 May 2021 - 6:31

77

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If for any sequence $\vec{r_n}\to\vec{a}$, the sequence $f(\vec{r_n})$ converges to $L$, prove that $\lim_{\vec{r} \to \vec{a}} f(\vec{r}) = L$

Published on 18 May 2021 - 13:40

55

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How did they get the final result here?

Published on 13 Jun 2021 - 14:26

50

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Can I swap the positions in this equation?

Published on 13 Jun 2021 - 20:07

98

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Clarifying Eq. 101 in The Matrix Cookbook

Published on 16 Jun 2021 - 22:25

219

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Gradient of inner product containing inverse of the sum of two matrices

Published on 02 Jul 2021 - 10:11

24

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Reason for a lower gradient value

Published on 05 Jul 2021 - 22:47

List Question

Can the gradient exist for a function of $n + 1$ variables?

Confused about computing the gradient of least-squares cost

What is the gradient of $x^T A\, x$ with respect to the matrix $A$?

Finding Potential for specific Vector Field, help?

Matrix differentiation, $x^T A x$ w.r.t $A$

Is there a bundle concept that includes tensors and spinors as special cases?

Partial derivative of $x_1^TAB^Tx_2$

Prove that there exists no scalar field which has derivative $> 0$ at a fixed point wrt every direction

If $f(x) \leq f(a)$ for all $x$ in an open ball $B(a)$ , then prove that $\nabla f(a) = 0$

If for any sequence $\vec{r_n}\to\vec{a}$, the sequence $f(\vec{r_n})$ converges to $L$, prove that $\lim_{\vec{r} \to \vec{a}} f(\vec{r}) = L$

How did they get the final result here?

Can I swap the positions in this equation?

Clarifying Eq. 101 in The Matrix Cookbook

Gradient of inner product containing inverse of the sum of two matrices

Reason for a lower gradient value

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