List questions from matrix-norms

Published on 19 Mar 2021 - 4:12

222

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How calculate the trace norm via convex optimization?

Published on 25 Mar 2026 - 12:55

1.1k

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What does it mean for an inner product to induce a norm?

Published on 21 Mar 2021 - 18:33

642

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Proof verification for matrix norm

Published on 24 Mar 2021 - 10:17

94

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Problem on unitary matrix

Published on 26 Mar 2026 - 22:19

142

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Relation between spectral norm and entries of a matrix

Published on 25 Mar 2026 - 19:04

490

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Why is the $\ell_1$-norm on $M_n$ is matrix norm that is not an induced norm?

Published on 09 Apr 2021 - 8:06

70

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Frobenius norm inequality: If $A \succ 0$ and $\| r \|_F < \|R \|_F$, can we conclude: $\| A^{-1/2} r A^{1/2} \|_F \leq \| A^{-1/2} R A^{1/2} \|_F$

Published on 11 Apr 2021 - 18:07

69

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What does this matrix operator norm mean?

Published on 14 Apr 2021 - 14:04

504

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About condition number

Published on 25 Mar 2026 - 17:35

100

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Is there a norm equivalent to the $\sup\{Lx : |x|=1\}$ norm for linear maps?

Published on 20 Apr 2021 - 10:24

80

Views

bounded spectral norm of $\left(\frac{1}{n} A A^{H}-z I_{m \times m}\right)^{-1}$ for any complex-valued with a nonzero imaginary part.

Published on 25 Mar 2026 - 17:42

321

Views

Why is the maximum value of $x^TAx$ is the largest eigenvalue of A?

Published on 26 Apr 2021 - 20:05

22

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Is the matrix norm of a $1$x$m$ matrix A the same as the vector norm of a $m$-dimensional row vector?

Published on 04 May 2021 - 6:43

586

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$2$-norm of a normal matrix

Published on 25 Mar 2026 - 19:02

List Question

A question on altering a definition of matrix norm

How calculate the trace norm via convex optimization?

What does it mean for an inner product to induce a norm?

Proof verification for matrix norm

Problem on unitary matrix

Relation between spectral norm and entries of a matrix

Why is the $\ell_1$-norm on $M_n$ is matrix norm that is not an induced norm?

Frobenius norm inequality: If $A \succ 0$ and $\| r \|_F < \|R \|_F$, can we conclude: $\| A^{-1/2} r A^{1/2} \|_F \leq \| A^{-1/2} R A^{1/2} \|_F$

What does this matrix operator norm mean?

About condition number

Is there a norm equivalent to the $\sup\{Lx : |x|=1\}$ norm for linear maps?

bounded spectral norm of $\left(\frac{1}{n} A A^{H}-z I_{m \times m}\right)^{-1}$ for any complex-valued with a nonzero imaginary part.

Why is the maximum value of $x^TAx$ is the largest eigenvalue of A?

Is the matrix norm of a $1$x$m$ matrix A the same as the vector norm of a $m$-dimensional row vector?

$2$-norm of a normal matrix

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