Question

Determine if two norms are equivalent.

score 429 · Answer 1 · 2026-02-23 04:36:29

429

Views

Determine if two norms are equivalent.

Published on 23 Feb 2026 - 4:36

score 503 · Answer 2 · 2018-10-21 13:25:05

503

Views

What is the purpose of differentiating between norms and metrics?

Published on 21 Oct 2018 - 13:25

score 607 · Answer 3 · 2026-03-27 14:52:53

607

Views

Show that if the norms $\| \cdot \|_1$ and $\| \cdot \|_2$ are equivalent, then $(X, \| \cdot \|_1)$ is Banach iff $(X, \| \cdot \|_2)$ is Banach

Published on 27 Mar 2026 - 14:52

score 917 · Answer 4 · 2018-10-21 19:17:34

917

Views

Every metric on a finite-dimensional vector space is equivalent

Published on 21 Oct 2018 - 19:17

score 677 · Answer 5 · 2026-03-25 17:36:53

677

Views

How to expand function with summation and equation inside the L2-norm?

Published on 25 Mar 2026 - 17:36

score 36 · Answer 6 · 2018-10-22 07:57:42

Limit of the $r$-norm $(\sum_{i=0}^n (y_1,x_i)-(y_2,x_i))^r )^{1/r}$ as $r \to \infty$ is $ \max_i \left|(y_1,x_i)-(y_2,x_i)\right| $

score 684 · Answer 7 · 2026-03-28 08:36:34

684

Views

Is $\Vert x \Vert_{H^m(\Omega)} = 1$ (Sobolev-norms) always a unit ball if you plot/visualise it it?

Published on 28 Mar 2026 - 8:36

score 192 · Answer 8 · 2018-10-22 19:38:58

192

Views

Proving $\lim_{p\to\infty} $ $\left\lVert x \right\rVert_p = \left\lVert x \right\rVert_\infty$

Published on 22 Oct 2018 - 19:38

score 142 · Answer 9 · 2026-03-25 23:37:56

142

Views

Proving real inclusion for $1 \leq p \lt r \lt \infty$

Published on 25 Mar 2026 - 23:37

score 226 · Answer 10 · 2018-10-23 06:18:17

226

Views

$\left\lVert x \right\rVert_p$ = ($\sum_{i=1}^{n} |x_i|^p$)$^{1/p}$ and triangle inequality

Published on 23 Oct 2018 - 6:18

score 43 · Answer 11 · 2018-10-23 07:04:59

43

Views

Proving that $\left\lVert x \right\rVert_a := \sum_{k=1}^{\infty}\ |x_k| $ defines a norm on a set

Published on 23 Oct 2018 - 7:04

score 1.6k · Answer 12 · 2018-10-23 12:11:52

1.6k

Views

Showing the existence of at least one unbounded linear operator

Published on 23 Oct 2018 - 12:11

score 42 · Answer 13 · 2026-03-28 02:41:03

42

Views

Solving a sign-constrained linear system

Published on 28 Mar 2026 - 2:41

score 49 · Answer 14 · 2026-03-27 13:24:30

49

Views

Showing that $(Y, \| \cdot \|)$ is Banach, iff $Y \subset (X,\| \cdot \|)$ is closed.

Published on 27 Mar 2026 - 13:24

score 131 · Answer 15 · 2026-03-28 22:31:05

131

Views

Can $n+1$ distinct positive vectors in $\mathbb{R}^n_{>0}$ agree on $n$ distinct weighted $p$-norms?

Published on 28 Mar 2026 - 22:31

List Question

Determine if two norms are equivalent.

What is the purpose of differentiating between norms and metrics?

Show that if the norms $\| \cdot \|_1$ and $\| \cdot \|_2$ are equivalent, then $(X, \| \cdot \|_1)$ is Banach iff $(X, \| \cdot \|_2)$ is Banach

Every metric on a finite-dimensional vector space is equivalent

How to expand function with summation and equation inside the L2-norm?

Limit of the $r$-norm $(\sum_{i=0}^n (y_1,x_i)-(y_2,x_i))^r )^{1/r}$ as $r \to \infty$ is $ \max_i \left|(y_1,x_i)-(y_2,x_i)\right| $

Is $\Vert x \Vert_{H^m(\Omega)} = 1$ (Sobolev-norms) always a unit ball if you plot/visualise it it?

Proving $\lim_{p\to\infty} $ $\left\lVert x \right\rVert_p = \left\lVert x \right\rVert_\infty$

Proving real inclusion for $1 \leq p \lt r \lt \infty$

$\left\lVert x \right\rVert_p$ = ($\sum_{i=1}^{n} |x_i|^p$)$^{1/p}$ and triangle inequality

Proving that $\left\lVert x \right\rVert_a := \sum_{k=1}^{\infty}\ |x_k| $ defines a norm on a set

Showing the existence of at least one unbounded linear operator

Solving a sign-constrained linear system

Showing that $(Y, \| \cdot \|)$ is Banach, iff $Y \subset (X,\| \cdot \|)$ is closed.

Can $n+1$ distinct positive vectors in $\mathbb{R}^n_{>0}$ agree on $n$ distinct weighted $p$-norms?

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