List questions from matrix-norms

Published on 13 Dec 2019 - 20:11

158

Views

If $||AB-I||=\epsilon<1$ then $||A^{-1}-B||<||B||(\frac{\epsilon}{1-\epsilon})$

Published on 18 Dec 2019 - 2:10

69

Views

What if $\|A^2\|_\infty=\|A\|^2_\infty$?

Published on 20 Dec 2019 - 21:53

87

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If $A$ is non-singular then there exist $B$ singular close to it

Published on 20 Dec 2019 - 23:12

388

Views

Condition number of a diagonal matrix with norm not induced by an inner product

Published on 25 Mar 2026 - 6:34

72

Views

What does a large spectral norm mean?

Published on 25 Mar 2026 - 5:59

390

Views

"Almost Normal" Matrix and Gap between Spectral Radius/Norm

Published on 25 Mar 2026 - 9:40

55

Views

Show, for a real, symmetric matrix, that $\| A\|_2^2 \leq \frac{n-1}{n} \|A\|_F^2$.

Published on 25 Mar 2026 - 7:44

1000

Views

For symmetric $A$, show that $\lVert A \rVert_2 \leq \lVert A \rVert_\infty$

Published on 25 Mar 2026 - 7:48

37

Views

Suggest matrix $A$ with a maximal singular value of $5$

Published on 18 Jan 2020 - 15:45

138

Views

Understanding matrix norms and spectral radius

Published on 19 Jan 2020 - 19:54

1.7k

Views

Proof of Matrix Norm Inequality (Hadamard product)

Published on 30 Jan 2020 - 22:09

234

Views

Matrix norm exercises

Published on 31 Jan 2020 - 16:44

233

Views

Derivative d/dx of ||A*sigmoid(x)||^2,

Published on 16 Feb 2020 - 8:00

92

Views

Let $A$ be non singular, prove that $\frac{1}{\|A^{-1}\|} = \min_{\|x\| = 1} \|Ax\|$

Published on 17 Feb 2020 - 22:14

List Question

Inequality for the matrix infinity norm

If $||AB-I||=\epsilon<1$ then $||A^{-1}-B||<||B||(\frac{\epsilon}{1-\epsilon})$

What if $\|A^2\|_\infty=\|A\|^2_\infty$?

If $A$ is non-singular then there exist $B$ singular close to it

Condition number of a diagonal matrix with norm not induced by an inner product

What does a large spectral norm mean?

"Almost Normal" Matrix and Gap between Spectral Radius/Norm

Show, for a real, symmetric matrix, that $\| A\|_2^2 \leq \frac{n-1}{n} \|A\|_F^2$.

For symmetric $A$, show that $\lVert A \rVert_2 \leq \lVert A \rVert_\infty$

Suggest matrix $A$ with a maximal singular value of $5$

Understanding matrix norms and spectral radius

Proof of Matrix Norm Inequality (Hadamard product)

Matrix norm exercises

Derivative d/dx of ||A*sigmoid(x)||^2,

Let $A$ be non singular, prove that $\frac{1}{\|A^{-1}\|} = \min_{\|x\| = 1} \|Ax\|$

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