Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userInequalities for selected eigenvalues of the product of matrices
149
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The product of a Hermitian matrix and a positive semidefinite matrix has only real eigenvalues. We present bounds for sums of eigenvalues of such a product.
rate research
Read More
The authors analyze the asymptotics of eigenvalues of Toeplitz matrices with certain continuous and discontinuous symbols. In particular, the authors prove a conjecture of Levitin and Shargorodsky on the near-periodicity of Toeplitz eigenvalues.
Let $T=begin{bmatrix} X &Y 0 & Zend{bmatrix}$ be an $n$-square matrix, where $X, Z$ are $r$-square and $(n-r)$-square, respectively. Among other determinantal inequalities, it is proved $det(I_n+T^*T)ge det(I_r+X^*X)cdot det(I_{n-r}+Z^*Z)$ with equality holds if and only if $Y=0$.
Following the recent work of Jiang and Lin (Linear Algebra Appl. 585 (2020) 45--49), we present more results (bounds) on Harnack type inequalities for matrices in terms of majorization (i.e., in partial products) of eigenvalues and singular values. We discuss and compare the bounds derived through different ways. Jiang and Lins results imply Tungs version of Harnacks inequality (Proc. Amer. Math. Soc. 15 (1964) 375--381); our results %with simpler proofs are stronger and more general than Jiang and Lins. We also show some majorization inequalities concerning Cayley transforms. Some open problems on spectral norm and eigenvalues are proposed.
We present inequalities related to generalized matrix function for positive semidefinite block matrices. We introduce partial generalized matrix functions corresponding to partial traces and then provide an unified extension of the recent inequalities due to Choi [6], Lin [14] and Zhang et al. [5,19]. We demonstrate the applications of a positive semidefinite $3times 3$ block matrix, which motivates us to give a simple alternative proof of Dragomirs inequality and Kreins inequality.
We consider the Sobolev norms of the pointwise product of two functions, and estimate from above and below the constants appearing in two related inequalities.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
