List questions from matrix-norms

Published on 12 Apr 2023 - 20:15

59

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Proof of the following matrix norm inequality$\|A\|_F \leq \sqrt{n} \| A \|_2$

Published on 14 Apr 2023 - 16:27

42

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Let $v \in \mathbb{R}^n$ and $A=v^T$. Prove that $\| A \|_2=\| v\|_2$

Published on 15 Apr 2023 - 1:40

49

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For any matrix $A \in \mathbb{R}^{m \times n}$, $\| A \|_{\infty} = \max_{i}\sum_{j=1}^{n} |a_{ij}|$

Published on 15 Apr 2023 - 17:39

114

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Prove $\| A\|_2=\|A^T\|_2$

Published on 25 Mar 2026 - 11:09

30

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Find outliers from a matrix X using standard deviation and frobenius norm

Published on 22 Apr 2023 - 10:55

25

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Calculating the variance of the following dot product.

Published on 23 Apr 2023 - 2:10

50

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How to prove $\left\Vert\nabla \frac{f}{||\nabla f||+\epsilon}\right\Vert\leq {\rm constant}$?

Published on 23 Apr 2023 - 16:32

17

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Show that an infinity supnorm is equal to the biggest row sum of the matrix

Published on 14 Mar 2026 - 11:31

114

Views

Subgradient of the spectral norm

Published on 25 Mar 2026 - 4:38

66

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Show the norm of projection decreases as the vector dimension increases

Published on 25 Apr 2023 - 6:54

37

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Does a bound on the operator norm of a square matrix generalize to a rectangular matrix?

Published on 26 Apr 2023 - 1:12

88

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Prove that $\sum_{k=1}^n|\lambda_k(X)-\lambda_k(Y)|\leq\|X-Y\|_1$

Published on 26 Apr 2023 - 11:30

115

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Relation between matrix norms and contractions

Published on 27 Feb 2026 - 16:32

117

Views

Bound on minimum perturbation of eigenvalues, based on condition number

Published on 25 Mar 2026 - 13:05

List Question

Inequality on Frobenius norms of the difference of 2 matrices

Proof of the following matrix norm inequality$\|A\|_F \leq \sqrt{n} \| A \|_2$

Let $v \in \mathbb{R}^n$ and $A=v^T$. Prove that $\| A \|_2=\| v\|_2$

For any matrix $A \in \mathbb{R}^{m \times n}$, $\| A \|_{\infty} = \max_{i}\sum_{j=1}^{n} |a_{ij}|$

Prove $\| A\|_2=\|A^T\|_2$

Find outliers from a matrix X using standard deviation and frobenius norm

Calculating the variance of the following dot product.

How to prove $\left\Vert\nabla \frac{f}{||\nabla f||+\epsilon}\right\Vert\leq {\rm constant}$?

Show that an infinity supnorm is equal to the biggest row sum of the matrix

Subgradient of the spectral norm

Show the norm of projection decreases as the vector dimension increases

Does a bound on the operator norm of a square matrix generalize to a rectangular matrix?

Prove that $\sum_{k=1}^n|\lambda_k(X)-\lambda_k(Y)|\leq\|X-Y\|_1$

Relation between matrix norms and contractions

Bound on minimum perturbation of eigenvalues, based on condition number

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