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An $m \times n$ matrix $R$ with nonnegative entries is called row stochastic if the sum of entries on every row of $R$ is 1. Let $𝐌_{m, n}$ be the set of all $m \times n$ real matrices. For $A, B \in 𝐌_{m, n}$ , we say that $A$ is row Hadamard majorized by $B$ (denoted by $A ≺_{R H} B)$ if there exists an $m \times n$ row stochastic matrix $R$ such that $A = R \circ B$ , where $X \circ Y$ is the Hadamard product (entrywise product) of matrices $X, Y \in 𝐌_{m, n}$ . In this paper, we consider the concept of row Hadamard majorization as a relation on $𝐌_{m, n}$ and characterize the structure of all linear operators $T : 𝐌_{m, n} \to 𝐌_{m, n}$ preserving (or...

Sätze über Determinanten und Anwendung derselben zum Beweise der Sätze von Pascal und Brianchon.

Franz Mertens (1877)

Journal für die reine und angewandte Mathematik

Schatten norms of Toeplitz matrices with Fisher--Hartwig singularities.

Böttcher, Albrecht (2006)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Schur complements and Banachiewicz-Schur forms.

Tian, Yongge, Takane, Yoshio (2005)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Schur complements of diagonally dominant matrices

David Carlson, Thomas L. Markham (1979)

Czechoslovak Mathematical Journal

Schur complements of generally diagonally dominant matrices and a criterion for irreducibility of matrices.

Zhang, Cheng-Yi, Luo, Shuanghua, Xu, Chengxian, Jiang, Hongying (2009)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Schur complements of matrices with acyclic bipartite graphs.

Britz, T., Olesky, D.D., van den Driessche, P. (2005)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Schur multiplier characterization of a class of infinite matrices

A. Marcoci, L. Marcoci, L. E. Persson, N. Popa (2010)

Czechoslovak Mathematical Journal

Let $B_{w} (ℓ^{p})$ denote the space of infinite matrices $A$ for which $A (x) \in ℓ^{p}$ for all $x = {x_{k}}_{k = 1}^{\infty} \in ℓ^{p}$ with $| x_{k} | ↘ 0$ . We characterize the upper triangular positive matrices from $B_{w} (ℓ^{p})$ , $1 < p < \infty$ , by using a special kind of Schur multipliers and the G. Bennett factorization technique. Also some related results are stated and discussed.

Self-correcting iterative methods for computing $2$ -inverses

Stanimirović, Predrag S. (2003)

Archivum Mathematicum

In this paper we construct a few iterative processes for computing ${2}$ -inverses of a linear bounded operator. These algorithms are extensions of the corresponding algorithms introduced in [11] and a method from [8]. A few error estimates are derived.

Semigroups of finite matrices.

O.S. Rothaus (1994)

Semigroup forum

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