Question

Proving that every finite-dimensional normed space has the same norm as the euclidean n-dimensional space

score 134 · Answer 1 · 2019-01-09 12:23:43

134

Views

Proving that every finite-dimensional normed space has the same norm as the euclidean n-dimensional space

Published on 09 Jan 2019 - 12:23

score 193 · Answer 2 · 2019-01-09 14:50:07

193

Views

A measure of similarity of real vectors independent of their dimension

Published on 09 Jan 2019 - 14:50

score 480 · Answer 3 · 2019-01-10 06:47:09

480

Views

Operator norm of $T:l^{2}\rightarrow l^{1}$ where $Tx=(x_{1},x_{2}/2,x_{3}/3,x_{4}/4,...)$

Published on 10 Jan 2019 - 6:47

score 730 · Answer 4 · 2026-02-23 20:42:04

730

Views

On the supremum norm of matrices

Published on 23 Feb 2026 - 20:42

score 28 · Answer 5 · 2019-01-12 04:10:52

28

Views

On the sharpness of an inequality involving operator norm of invertible matrices

Published on 12 Jan 2019 - 4:10

score 124 · Answer 6 · 2026-03-25 17:40:36

124

Views

On an inequality involving operator norm of matrices and singular value

Published on 25 Mar 2026 - 17:40

score 309 · Answer 7 · 2026-03-29 19:11:12

309

Views

Minimizing $\ell_p$ distance to affine subspace of affine subspace

Published on 29 Mar 2026 - 19:11

score 207 · Answer 8 · 2019-01-13 18:30:37

207

Views

$C[0,1], 0<p<1$ is not a norm linear space. What about $p = \infty$ (i.e. supremum norm)?

Published on 13 Jan 2019 - 18:30

score 67 · Answer 9 · 2019-01-14 04:14:28

67

Views

How to show $\|A\|_2 \leq t$ implies $ t^2I-A^TA \succeq 0$?

Published on 14 Jan 2019 - 4:14

score 453 · Answer 10 · 2026-03-29 20:15:28

453

Views

Is the $p$-norm ever a norm for $0<p<1$?

Published on 29 Mar 2026 - 20:15

score 108 · Answer 11 · 2026-03-28 22:30:57

108

Views

compute the norm of a linear operator

Published on 28 Mar 2026 - 22:30

score 980 · Answer 12 · 2019-01-16 10:30:48

980

Views

Is $d(x,y)=\frac {\|x-y\|} {\sqrt {1+\|x\|^{2}}\sqrt {1+\|y\|^{2}}}$ a metric on a normed linear space?

Published on 16 Jan 2019 - 10:30

score 128 · Answer 13 · 2026-03-30 06:32:08

128

Views

Consider the order $\mathbb{Z}[\sqrt[4]{24}]$. Find all ideals of norm 100.

Published on 30 Mar 2026 - 6:32

score 3.2k · Answer 14 · 2019-01-16 18:20:12

3.2k

Views

Proving the Lp norm is a norm.

Published on 16 Jan 2019 - 18:20

score 446 · Answer 15 · 2019-01-16 20:02:12

446

Views

Can $\| \left( X'X + \lambda I \right) ^{-1} X'y \| = t$ be solved for $\lambda$?

Published on 16 Jan 2019 - 20:02

List Question

Proving that every finite-dimensional normed space has the same norm as the euclidean n-dimensional space

A measure of similarity of real vectors independent of their dimension

Operator norm of $T:l^{2}\rightarrow l^{1}$ where $Tx=(x_{1},x_{2}/2,x_{3}/3,x_{4}/4,...)$

On the supremum norm of matrices

On the sharpness of an inequality involving operator norm of invertible matrices

On an inequality involving operator norm of matrices and singular value

Minimizing $\ell_p$ distance to affine subspace of affine subspace

$C[0,1], 0<p<1$ is not a norm linear space. What about $p = \infty$ (i.e. supremum norm)?

How to show $\|A\|_2 \leq t$ implies $ t^2I-A^TA \succeq 0$?

Is the $p$-norm ever a norm for $0<p<1$?

compute the norm of a linear operator

Is $d(x,y)=\frac {\|x-y\|} {\sqrt {1+\|x\|^{2}}\sqrt {1+\|y\|^{2}}}$ a metric on a normed linear space?

Consider the order $\mathbb{Z}[\sqrt[4]{24}]$. Find all ideals of norm 100.

Proving the Lp norm is a norm.

Can $\| \left( X'X + \lambda I \right) ^{-1} X'y \| = t$ be solved for $\lambda$?

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