Question

Let $x_0,x_1,...,x_k$ be $k+1$ vectors. Find the number of multiplications in $\|x_0\|^2_2+\dotsb+\|x_k\|_2^2$

score 27 · Answer 1 · 2021-02-12 00:36:55

27

Views

Let $x_0,x_1,...,x_k$ be $k+1$ vectors. Find the number of multiplications in $\|x_0\|^2_2+\dotsb+\|x_k\|_2^2$

Published on 12 Feb 2021 - 0:36

score 916 · Answer 2 · 2026-02-23 10:47:45

916

Views

$2$-norm of a rank-$1$ matrix

Published on 23 Feb 2026 - 10:47

score 561 · Answer 3 · 2026-03-26 22:57:55

561

Views

Submultiplicity of matrix norm from the spectral radius $ + \epsilon$

Published on 26 Mar 2026 - 22:57

score 164 · Answer 4 · 2021-02-19 01:28:22

164

Views

Spectral Condition Number Bound

Published on 19 Feb 2021 - 1:28

score 43 · Answer 5 · 2021-02-25 10:43:55

43

Views

Show that $\|A(I - vv^T/v^Tv)\|_F^2 = \|A\|_F^2 - \|Av\|^2_2/(v^tv)$

Published on 25 Feb 2021 - 10:43

score 436 · Answer 6 · 2021-02-25 17:42:41

436

Views

Proving matrix norm to be submultiplicative?

Published on 25 Feb 2021 - 17:42

score 1.4k · Answer 7 · 2021-02-27 08:39:58

1.4k

Views

When is the operator norm inequality for matrix product an equality?

Published on 27 Feb 2021 - 8:39

score 97 · Answer 8 · 2021-03-02 06:15:01

97

Views

How to expand $\langle \textbf{x}-\textbf{y},\textbf{x}-\textbf{y}\rangle$ using the Cauchy–Schwarz inequality

Published on 02 Mar 2021 - 6:15

score 156 · Answer 9 · 2026-03-26 04:49:55

156

Views

contraction in five dimensional Euclidean space

Published on 26 Mar 2026 - 4:49

score 2.3k · Answer 10 · 2021-03-05 15:21:18

2.3k

Views

How to relate Frobenius norm and trace of a matrix?

Published on 05 Mar 2021 - 15:21

score 196 · Answer 11 · 2021-03-08 03:30:59

196

Views

finer topology and topology induced by norms

Published on 08 Mar 2021 - 3:30

score 336 · Answer 12 · 2021-03-13 19:52:54

336

Views

how can I find a orthogonal matrix Q such that Q$x_i=y_i$

Published on 13 Mar 2021 - 19:52

score 111 · Answer 13 · 2026-03-27 00:59:51

111

Views

Given $A \in \mathbb{R}^{n \times n}$ with spectral radius $\rho(A)<1$, is it possible for $||A||>1$ for Euclidean norm $|| \cdot ||$?

Published on 27 Mar 2026 - 0:59

score 382 · Answer 14 · 2026-03-25 12:48:54

382

Views

Maximize $\langle {\bf A} , {\bf X} \rangle$ subject to $\| {\bf X} \|_* \leq 1$

Published on 25 Mar 2026 - 12:48

score 269 · Answer 15 · 2026-03-25 23:39:23

269

Views

Smallest Lipschitz constant of $x \mapsto A_0 + \sum_{i=1}^n x_i A_i$

Published on 25 Mar 2026 - 23:39

List Question

Let $x_0,x_1,...,x_k$ be $k+1$ vectors. Find the number of multiplications in $\|x_0\|^2_2+\dotsb+\|x_k\|_2^2$

$2$-norm of a rank-$1$ matrix

Submultiplicity of matrix norm from the spectral radius $ + \epsilon$

Spectral Condition Number Bound

Show that $\|A(I - vv^T/v^Tv)\|_F^2 = \|A\|_F^2 - \|Av\|^2_2/(v^tv)$

Proving matrix norm to be submultiplicative?

When is the operator norm inequality for matrix product an equality?

How to expand $\langle \textbf{x}-\textbf{y},\textbf{x}-\textbf{y}\rangle$ using the Cauchy–Schwarz inequality

contraction in five dimensional Euclidean space

How to relate Frobenius norm and trace of a matrix?

finer topology and topology induced by norms

how can I find a orthogonal matrix Q such that Q$x_i=y_i$

Given $A \in \mathbb{R}^{n \times n}$ with spectral radius $\rho(A)<1$, is it possible for $||A||>1$ for Euclidean norm $|| \cdot ||$?

Maximize $\langle {\bf A} , {\bf X} \rangle$ subject to $\| {\bf X} \|_* \leq 1$

Smallest Lipschitz constant of $x \mapsto A_0 + \sum_{i=1}^n x_i A_i$

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