Question

Why are we able to define the Frobenius norm as so?

score 83 · Answer 1 · 2026-03-25 19:03:37

83

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Why are we able to define the Frobenius norm as so?

Published on 25 Mar 2026 - 19:03

score 223 · Answer 2 · 2026-03-25 17:41:51

223

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Upper-bound for nuclear norm of $A \circ (v \otimes v)$ in terms of operator norm (or nuclear norm) of matrix $A$ and $L_\infty$-norm of vector $v$.

Published on 25 Mar 2026 - 17:41

score 42 · Answer 3 · 2021-12-04 06:33:29

42

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Show that $||A-BC||_F^2 = ||A||_F^2+||BC||_F^2 - 2tr(C^TB^TA)$

Published on 04 Dec 2021 - 6:33

score 234 · Answer 4 · 2026-03-26 01:26:58

234

Views

Jacobi preconditioner versus unit-row or unit-column preconditioner

Published on 26 Mar 2026 - 1:26

score 172 · Answer 5 · 2021-12-17 07:43:12

172

Views

How to calculate Norm for a Polynomial in P(R) of (1+x)

Published on 17 Dec 2021 - 7:43

score 32 · Answer 6 · 2021-12-27 08:56:45

32

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Frobenius norm equality related to "orthonormal pair"

Published on 27 Dec 2021 - 8:56

score 109 · Answer 7 · 2026-03-27 11:46:49

109

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Is the truncated Frobenius norm convex or not?

Published on 27 Mar 2026 - 11:46

score 80 · Answer 8 · 2021-12-29 00:47:27

80

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Proving $||A^{-1} v || \geq ||A^{-1} u ||$ implies $||v|| \geq ||u||$.

Published on 29 Dec 2021 - 0:47

score 1.2k · Answer 9 · 2026-02-23 13:10:51

1.2k

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Prove $\frac{1}{\sqrt{n}}\|A\|_{\infty} \leq\|A\|_{2} \leq \sqrt{m}\|A\|_{\infty} $

Published on 23 Feb 2026 - 13:10

score 52 · Answer 10 · 2022-01-02 20:28:42

52

Views

Average square gain of a matrix over all possible vectors

Published on 02 Jan 2022 - 20:28

score 45 · Answer 11 · 2022-01-03 18:21:08

45

Views

$\lim_{x\to\infty} K_{ij}(x) = 0$ BUT $\lim_{x\to\infty} ||K(x)||_{F} = \sqrt{n-1}$ !!!

Published on 03 Jan 2022 - 18:21

score 251 · Answer 12 · 2022-01-04 18:50:30

251

Views

How do we know that the Frobenius norm is not subordinate to a vector norm?

Published on 04 Jan 2022 - 18:50

score 32 · Answer 13 · 2022-01-06 20:02:22

32

Views

Limiting the inverse of a block matrix based on how small the non-diagonal blocks are, if the diagonal ones are positive definite?

Published on 06 Jan 2022 - 20:02

score 83 · Answer 14 · 2026-03-25 23:42:46

83

Views

If $A = R R^T$, prove that $||R_1 R_1^T||_2 \le ||A||_2$ where $R_1$ is first column of $R$.

Published on 25 Mar 2026 - 23:42

score 472 · Answer 15 · 2022-01-08 20:48:34

472

Views

The Frobenius norm is submultiplicative

Published on 08 Jan 2022 - 20:48

List Question

Why are we able to define the Frobenius norm as so?

Upper-bound for nuclear norm of $A \circ (v \otimes v)$ in terms of operator norm (or nuclear norm) of matrix $A$ and $L_\infty$-norm of vector $v$.

Show that $||A-BC||_F^2 = ||A||_F^2+||BC||_F^2 - 2tr(C^TB^TA)$

Jacobi preconditioner versus unit-row or unit-column preconditioner

How to calculate Norm for a Polynomial in P(R) of (1+x)

Frobenius norm equality related to "orthonormal pair"

Is the truncated Frobenius norm convex or not?

Proving $||A^{-1} v || \geq ||A^{-1} u ||$ implies $||v|| \geq ||u||$.

Prove $\frac{1}{\sqrt{n}}\|A\|_{\infty} \leq\|A\|_{2} \leq \sqrt{m}\|A\|_{\infty} $

Average square gain of a matrix over all possible vectors

$\lim_{x\to\infty} K_{ij}(x) = 0$ BUT $\lim_{x\to\infty} ||K(x)||_{F} = \sqrt{n-1}$ !!!

How do we know that the Frobenius norm is not subordinate to a vector norm?

Limiting the inverse of a block matrix based on how small the non-diagonal blocks are, if the diagonal ones are positive definite?

If $A = R R^T$, prove that $||R_1 R_1^T||_2 \le ||A||_2$ where $R_1$ is first column of $R$.

The Frobenius norm is submultiplicative

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