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### ${𝒟}_{n,r}$ 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.

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

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

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

Applied Mathematics E-Notes [electronic only]

### 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 characterization of strong regularity of interval matrices.

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

### A common recursion for Laplacians of matroids and shifted simplicial complexes.

Documenta Mathematica

### A Computational Method for Eigenvalues and Eigenvectors of a Matrix with Real Eigenvalues.

Numerische Mathematik

### A convergence criterion for multiple ratios

Portugaliae mathematica

### A Convergent Jacobi Method for Solving the Eigenproblem of Arbitrary Real Matrices.

Numerische Mathematik

### A deflation formula for tridiagonal matrices

Aplikace matematiky

An explicit formula for the deflation of a tridiagonal matrix is presented. The resulting matrix is again tridiagonal.

### A fast algorithm for solving regularized total least squares problems.

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

### A formula for all minors of the adjacency matrix and an application

Special Matrices

We supply a combinatorial description of any minor of the adjacency matrix of a graph. This description is then used to give a formula for the determinant and inverse of the adjacency matrix, A(G), of a graph G, whenever A(G) is invertible, where G is formed by replacing the edges of a tree by path bundles.

### A formula for the eigenvalues of a compact operator

Studia Mathematica

### A geometric maximization problem

The Teaching of Mathematics

### A geometric proof of the Perron-Frobenius theorem.

We obtain an elementary geometrical proof of the classical Perron-Frobenius theorem for non-negative matrices A by using the Brouwer fixed-point theorem and by studying the dynamics of the action of A on convenient subsets of Rn.

### A. Horn's result on matrices with prescribed singular values and eigenvalues.

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

### A Jacobi Type Method for Complex Symmetric Matrices.

Numerische Mathematik

### A matrix inequality for Möbius functions.

JIPAM. Journal of Inequalities in Pure &amp; Applied Mathematics [electronic only]

### A method for the Eigenreduction of real Symmetric Matrices

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

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