2
votes
1answer
286 views

Null Space Perturbations

Hi, I face a problem some time now (not a homework problem) and I believe it is related to matrix perturbations and how the null space behaves in these cases. The distilled version of the ...
1
vote
2answers
904 views

submultiplicity of matrix norm. Is $||AB||_F \leq ||A||_2||B||_F$?

Let $||\cdot||_F$ and $||\cdot||_2$ be the Frobenius norm and the spectral norm. I'm reading Ji-Guang Sun's paper 'Perturbation Bounds for the Cholesky and QR Factorizations' from BIT 31 in 1991. ...
3
votes
0answers
284 views

A question about the generalized Lidskii-Wielandt inequality for matrices proved by Thompson and Freede

In 1971, Thomson and Freede generalized the Lidskii-Wielandt inequalites as follows (version for singular values) Let $A$, $B$ be $n\times n$ Hermitian matrices. Suppose $\alpha_1\geq \alpha_2 \geq ...