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### $\left(0,1\right)$-matrices, discrepancy and preservers

Czechoslovak Mathematical Journal

Let $m$ and $n$ be positive integers, and let $R=\left({r}_{1},...,{r}_{m}\right)$ and $S=\left({s}_{1},...,{s}_{n}\right)$ be nonnegative integral vectors. Let $A\left(R,S\right)$ be the set of all $m×n$$\left(0,1\right)$-matrices with row sum vector $R$ and column vector...

### ${ℤ}_{k+l}×{ℤ}_{2}$-graded polynomial identities for ${M}_{k,l}\left(E\right)\otimes E$

Rendiconti del Seminario Matematico della Università di Padova

### $\left(m,r\right)$-central Riordan arrays and their applications

Czechoslovak Mathematical Journal

For integers $m>r\ge 0$, Brietzke (2008) defined the $\left(m,r\right)$-central coefficients of an infinite lower triangular matrix $G=\left(d,h\right)={\left({d}_{n,k}\right)}_{n,k\in ℕ}$ as ${d}_{mn+r,\left(m-1\right)n+r}$, with $n=0,1,2,\cdots$, and the $\left(m,r\right)$-central coefficient triangle of $G$ as ${G}^{\left(m,r\right)}={\left({d}_{mn+r,\left(m-1\right)n+k+r}\right)}_{n,k\in ℕ}.$ It is known that the $\left(m,r\right)$-central coefficient triangles of any Riordan array are also Riordan arrays. In this paper, for a Riordan array $G=\left(d,h\right)$ with $h\left(0\right)=0$ and $d\left(0\right),{h}^{\text{'}}\left(0\right)\ne 0$, we obtain the generating function of its $\left(m,r\right)$-central coefficients and give an explicit representation for the $\left(m,r\right)$-central Riordan array ${G}^{\left(m,r\right)}$ in terms of the Riordan array $G$. Meanwhile, the...

### ${𝒟}_{n,r}$ is not potentially nilpotent for $n\ge 4r-2$

Czechoslovak Mathematical Journal

An $n×n$ sign pattern $𝒜$ is said to be potentially nilpotent if there exists a nilpotent real matrix $B$ with the same sign pattern as $𝒜$. Let ${𝒟}_{n,r}$ be an $n×n$ sign pattern with $2\le r\le n$ such that the superdiagonal and the $\left(n,n\right)$ entries are positive, the $\left(i,1\right)$$\left(i=1...$

### $±$ sign pattern matrices that allow orthogonality

Czechoslovak Mathematical Journal

A sign pattern $A$ is a $±$ sign pattern if $A$ has no zero entries. $A$ allows orthogonality if there exists a real orthogonal matrix $B$ whose sign pattern equals $A$. Some sufficient conditions are given for a sign pattern matrix to allow orthogonality, and a complete characterization is given for $±$ sign patterns with $n-1\le {N}_{-}\left(A\right)\le n+1$ to allow orthogonality.

### 150 let od objevu kvaternionů

Pokroky matematiky, fyziky a astronomie

### 2-innerproduct spaces and Gâteaux partial derivatives

Commentationes Mathematicae Universitatis Carolinae

### 4-Dimensional (Para)-Kähler-Weyl Structures

Publications de l'Institut Mathématique

### A 1-norm bound for inverses of triangular matrices with monotone entries.

Banach Journal of Mathematical Analysis [electronic only]

### A basic decomposition result related to the notion of the rank of a matrix and applications.

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

### A basis of the conjunctively polynomial-like Boolean functions.

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

### A basis of the set of sequences satisfying a given m-th order linear recurrence.

Elemente der Mathematik

### A Bound Connected with Primitive Matrices.

Numerische Mathematik

### A bound for the Moore-Penrose pseudoinverse of a matrix

Commentationes Mathematicae Universitatis Carolinae

### A bound for the rank-one transient of inhomogeneous matrix products in special case

Kybernetika

We consider inhomogeneous matrix products over max-plus algebra, where the matrices in the product satisfy certain assumptions under which the matrix products of sufficient length are rank-one, as it was shown in  (Shue, Anderson, Dey 1998). We establish a bound on the transient after which any product of matrices whose length exceeds that bound becomes rank-one.

### A bound for the spectral variation of two matrices.

Applied Mathematics E-Notes [electronic only]

### A boundary-value problem for linear PDAEs

International Journal of Applied Mathematics and Computer Science

We analyze a boundary-value problem for linear partial differential algebraic equations, or PDAEs, by using the method of the separation of variables. The analysis is based on the Kronecker-Weierstrass form of the matrix pencil[A,-λ_n B]. A new theorem is proved and two illustrative examples are given.

### A Brauer’s theorem and related results

Open Mathematics

Given a square matrix A, a Brauer’s theorem [Brauer A., Limits for the characteristic roots of a matrix. IV. Applications to stochastic matrices, Duke Math. J., 1952, 19(1), 75–91] shows how to modify one single eigenvalue of A via a rank-one perturbation without changing any of the remaining eigenvalues. Older and newer results can be considered in the framework of the above theorem. In this paper, we present its application to stabilization of control systems, including the case when the system...

### A Bruhat order for the class of $\left(0,1\right)$-matrices with row sum vector $R$ and column sum vector $S$.

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

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