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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 $Y=0$.
Denote by $P_n$ the set of $ntimes n$ positive definite matrices. Let $D = D_1oplus dots oplus D_k$, where $D_1in P_{n_1}, dots, D_k in P_{n_k}$ with $n_1+cdots + n_k=n$. Partition $Cin P_n$ according to $(n_1, dots, n_k)$ so that $Diag C = C_1oplus
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. W
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.
Entrywise powers of matrices have been well-studied in the literature, and have recently received renewed attention in the regularization of high-dimensional correlation matrices. In this paper, we study powers of positive semidefinite block matrices
A Banach space operator $Tin B({cal X})$ is polaroid if points $lambdainisosigmasigma(T)$ are poles of the resolvent of $T$. Let $sigma_a(T)$, $sigma_w(T)$, $sigma_{aw}(T)$, $sigma_{SF_+}(T)$ and $sigma_{SF_-}(T)$ denote, respectively, the approximat