Question

If $\mathbf{v}\in\mathbb{C}^n$, does $\sum_{k=1}^{n}v_k^2$ has any specific name?

score 42 · Answer 1 · 2020-07-21 16:11:51

42

Views

If $\mathbf{v}\in\mathbb{C}^n$, does $\sum_{k=1}^{n}v_k^2$ has any specific name?

Published on 21 Jul 2020 - 16:11

score 43 · Answer 2 · 2020-07-21 19:16:50

43

Views

Does $g(v_n) \longrightarrow g(0)$ for all $v_n \text{s.t.} ||v_{n+1}|| \leq ||v_n||$ imply $g$ continuos at $0$?

Published on 21 Jul 2020 - 19:16

score 564 · Answer 3 · 2026-03-29 05:50:15

564

Views

In infinite dimensions, is it possible that convergence of distances to a sequence always implies convergence of that sequence?

Published on 29 Mar 2026 - 5:50

score 246 · Answer 4 · 2026-03-28 11:27:04

246

Views

All norm in a finite dimensional topological space are equivalent

Published on 28 Mar 2026 - 11:27

score 142 · Answer 5 · 2026-04-12 10:11:03

142

Views

How does this function arrive while formulating the auxiliary inequality for proof of $\mathcal {L^p}$ as a metric space?

Published on 12 Apr 2026 - 10:11

score 406 · Answer 6 · 2026-03-30 09:53:50

406

Views

Least squares coordinate-wise smoothness

Published on 30 Mar 2026 - 9:53

score 252 · Answer 7 · 2026-04-13 13:47:15

252

Views

Matrix Norm With Respect to Another Matrix?

Published on 13 Apr 2026 - 13:47

score 255 · Answer 8 · 2026-03-25 17:44:44

255

Views

If $v_1,v_2,\ldots,v_n\in \mathbb{R}^n$ s.t $\|v_k\|=1$, then $\exists\epsilon_k=\pm 1$ s.t. $\left\|\sum_{k=1}^n \epsilon_k v_k\right\|\le \sqrt{n}$.

Published on 25 Mar 2026 - 17:44

score 78 · Answer 9 · 2026-04-12 22:15:58

78

Views

Equivalence in the definitions of isometric and and isometric isomorphism.

Published on 12 Apr 2026 - 22:15

score 97 · Answer 10 · 2026-04-09 21:19:45

97

Views

Inequality involving 1-norm, discrete Wasserstein distance and majorization

Published on 09 Apr 2026 - 21:19

score 67 · Answer 11 · 2026-03-26 06:07:08

67

Views

Help to prove the following inequality with the matrix max norm?

Published on 26 Mar 2026 - 6:07

score 339 · Answer 12 · 2026-04-09 11:21:14

339

Views

how to check triangle inequality in definition of norm

Published on 09 Apr 2026 - 11:21

score 23 · Answer 13 · 2020-07-25 14:02:39

23

Views

Source for if $L_A:(\mathbb{R}^n, \left\Vert \cdot \right\Vert_p) \to (\mathbb{R}^n, \left\Vert \cdot \right\Vert_q)$ is an isometry, then $p = q$.

Published on 25 Jul 2020 - 14:02

score 28 · Answer 14 · 2026-04-07 00:02:09

28

Views

Does function $f(x,y,z) = \frac{1}{\|\mathbf{x}\|}+\sin(x^2y)\cos(z-7)$ belong to space $L^k(B)$ for $k = 1, 2, 3, 4$?

Published on 07 Apr 2026 - 0:02

score 673 · Answer 15 · 2026-03-26 22:55:41

673

Views

Is it true that the infinity norm of the matrix exponential $\|e^{At}\|_{l^\infty} \leq 1$ if $A$ is a negative diagonally dominant matrix?

Published on 26 Mar 2026 - 22:55

List Question

If $\mathbf{v}\in\mathbb{C}^n$, does $\sum_{k=1}^{n}v_k^2$ has any specific name?

Does $g(v_n) \longrightarrow g(0)$ for all $v_n \text{s.t.} ||v_{n+1}|| \leq ||v_n||$ imply $g$ continuos at $0$?

In infinite dimensions, is it possible that convergence of distances to a sequence always implies convergence of that sequence?

All norm in a finite dimensional topological space are equivalent

How does this function arrive while formulating the auxiliary inequality for proof of $\mathcal {L^p}$ as a metric space?

Least squares coordinate-wise smoothness

Matrix Norm With Respect to Another Matrix?

If $v_1,v_2,\ldots,v_n\in \mathbb{R}^n$ s.t $\|v_k\|=1$, then $\exists\epsilon_k=\pm 1$ s.t. $\left\|\sum_{k=1}^n \epsilon_k v_k\right\|\le \sqrt{n}$.

Equivalence in the definitions of isometric and and isometric isomorphism.

Inequality involving 1-norm, discrete Wasserstein distance and majorization

Help to prove the following inequality with the matrix max norm?

how to check triangle inequality in definition of norm

Source for if $L_A:(\mathbb{R}^n, \left\Vert \cdot \right\Vert_p) \to (\mathbb{R}^n, \left\Vert \cdot \right\Vert_q)$ is an isometry, then $p = q$.

Does function $f(x,y,z) = \frac{1}{\|\mathbf{x}\|}+\sin(x^2y)\cos(z-7)$ belong to space $L^k(B)$ for $k = 1, 2, 3, 4$?

Is it true that the infinity norm of the matrix exponential $\|e^{At}\|_{l^\infty} \leq 1$ if $A$ is a negative diagonally dominant matrix?

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