Question

In a infinite dimensional normed vector space $W=V \oplus U$ with $U$ finite dimensional, is the projection of $W$ on $V$ bounded?

score 92 · Answer 1 · 2026-03-26 08:02:39

92

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In a infinite dimensional normed vector space $W=V \oplus U$ with $U$ finite dimensional, is the projection of $W$ on $V$ bounded?

Published on 26 Mar 2026 - 8:02

score 2.5k · Answer 2 · 2018-04-06 21:02:46

2.5k

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Prove $u$ is a unit if and only if $N(u) = 1$?

Published on 06 Apr 2018 - 21:02

score 3k · Answer 3 · 2026-03-20 04:01:15

3k

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Definition of a Euclidean domain

Published on 20 Mar 2026 - 4:01

score 372 · Answer 4 · 2018-04-07 11:46:42

372

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Frobenius norm of $n \times n$ matrix

Published on 07 Apr 2018 - 11:46

score 1.1k · Answer 5 · 2018-04-07 14:57:51

1.1k

Views

Gradient of a norm function

Published on 07 Apr 2018 - 14:57

score 50 · Answer 6 · 2026-03-25 22:05:24

50

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What are the requirements on the function f(x) for the L_2 norm of f(x) to be a convex function?

Published on 25 Mar 2026 - 22:05

score 191 · Answer 7 · 2026-03-25 02:56:42

191

Views

Multiplicative absolute value

Published on 25 Mar 2026 - 2:56

score 70 · Answer 8 · 2018-04-08 06:54:46

70

Views

Infinite-dimensional normed space meaning

Published on 08 Apr 2018 - 6:54

score 87 · Answer 9 · 2018-04-08 09:22:26

87

Views

Proving the inequality $\|A\|_2 ^2 \le \|A\|_1 \|A\|_\infty$

Published on 08 Apr 2018 - 9:22

score 46 · Answer 10 · 2018-04-08 12:30:27

46

Views

Vector norm in $\mathbb{C}^n$

Published on 08 Apr 2018 - 12:30

score 57 · Answer 11 · 2026-03-25 11:52:55

57

Views

Normed spaces and closed sets.

Published on 25 Mar 2026 - 11:52

score 364 · Answer 12 · 2026-03-26 20:16:58

364

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In $\mathbb{R}^{n \times n}$, $AB$ and $BA$ have the same eigenvalues and Frobenius norm.

Published on 26 Mar 2026 - 20:16

score 185 · Answer 13 · 2026-03-25 12:21:12

185

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Proof of : Norm of Linear transformation from Rn (equipped with sup-norm) to Rm (equipped with l1 norm)

Published on 25 Mar 2026 - 12:21

score 591 · Answer 14 · 2018-04-09 07:12:09

591

Views

What does it mean for all norms are elementwise over matrix entries

Published on 09 Apr 2018 - 7:12

score 2.1k · Answer 15 · 2026-03-22 02:09:32

2.1k

Views

Prove that nuclear norm of a matrix is equal to the sum of squares of Frobenius norm

Published on 22 Mar 2026 - 2:09

List Question

In a infinite dimensional normed vector space $W=V \oplus U$ with $U$ finite dimensional, is the projection of $W$ on $V$ bounded?

Prove $u$ is a unit if and only if $N(u) = 1$?

Definition of a Euclidean domain

Frobenius norm of $n \times n$ matrix

Gradient of a norm function

What are the requirements on the function f(x) for the L_2 norm of f(x) to be a convex function?

Multiplicative absolute value

Infinite-dimensional normed space meaning

Proving the inequality $\|A\|_2 ^2 \le \|A\|_1 \|A\|_\infty$

Vector norm in $\mathbb{C}^n$

Normed spaces and closed sets.

In $\mathbb{R}^{n \times n}$, $AB$ and $BA$ have the same eigenvalues and Frobenius norm.

Proof of : Norm of Linear transformation from Rn (equipped with sup-norm) to Rm (equipped with l1 norm)

What does it mean for all norms are elementwise over matrix entries

Prove that nuclear norm of a matrix is equal to the sum of squares of Frobenius norm

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