List questions from spectral-norm

50

Views

Show $||U_i-V_i||\leq\epsilon\ \ \forall i=1,...,m\Longrightarrow||U_m...U_1-V_m...V_1||\leq m\epsilon$ (spectral norm)

Published on 19 Jan 2019 - 2:01

391

Views

Are the eigenvalues of a matrix and just its diagonal related?

Published on 22 Jan 2019 - 8:18

1k

Views

What is the Hessian of the spectral norm?

Published on 21 Mar 2026 - 15:15

209

Views

About a spectral norm estimation

Published on 27 Feb 2019 - 8:20

79

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Derive Lipschitz norm equality.

Published on 03 Mar 2019 - 5:47

483

Views

A direct result from the definition of operator norm: $\|Av\|\leq \|A\|_{op} \|v\|$

Published on 05 Mar 2019 - 17:53

1.5k

Views

For an orthogonal matrix $Q$, prove $\operatorname{cond}(Q)=1$

Published on 08 Mar 2019 - 19:19

56

Views

Example of a matrix where equality occurs for the relation between infinite and 2 norm

Published on 17 Mar 2019 - 10:02

264

Views

Show that the spectral norm of one matrix is smaller than the other.

Published on 19 Mar 2019 - 17:57

963

Views

Submultiplicavity of spectral norm

Published on 22 Mar 2019 - 15:02

355

Views

Limit of log of norm of exponential of Hamiltonian Matrix equals maximal eigenvalue

Published on 25 Mar 2019 - 5:37

370

Views

Spectral norm and inner product

Published on 29 Mar 2019 - 23:44

341

Views

Bound $|x^TAy|$ in terms of $\|A\|$ and $|x^Ty|$

Published on 16 Apr 2019 - 8:13

397

Views

Eigenvectors of sum of Hermitian matrices

Published on 01 May 2019 - 15:03

132

Views

Eigenvalues decrease with power

Published on 19 May 2019 - 11:23

List Question

Show $||U_i-V_i||\leq\epsilon\ \ \forall i=1,...,m\Longrightarrow||U_m...U_1-V_m...V_1||\leq m\epsilon$ (spectral norm)

Are the eigenvalues of a matrix and just its diagonal related?

What is the Hessian of the spectral norm?

About a spectral norm estimation

Derive Lipschitz norm equality.

A direct result from the definition of operator norm: $\|Av\|\leq \|A\|_{op} \|v\|$

For an orthogonal matrix $Q$, prove $\operatorname{cond}(Q)=1$

Example of a matrix where equality occurs for the relation between infinite and 2 norm

Show that the spectral norm of one matrix is smaller than the other.

Submultiplicavity of spectral norm

Limit of log of norm of exponential of Hamiltonian Matrix equals maximal eigenvalue

Spectral norm and inner product

Bound $|x^TAy|$ in terms of $\|A\|$ and $|x^Ty|$

Eigenvectors of sum of Hermitian matrices

Eigenvalues decrease with power

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