In this paper we consider the classical system of matrix equationsover , an arbitrary regular ring with identity. Necessary and sufficient conditions for the existence and the expression of the general solution to the system are derived. As an application, the linear matrix equation + = over is...

Earlier results expressing multivariate subresultants as ratios of two subdeterminants of the Macaulay matrix are extended to Jouanolou's resultant matrices. These matrix constructions are generalizations of the classical Macaulay matrices and involve matrices of significantly smaller size....

This paper proposes a simple approach for the matrix inversion. The number of the steps is equal to the order of the matrix to be inverted. The algorithm was arise as a “side product” during an analysis of the properties of the Guyan reduction (, (2) (1965) 380). Numerical tests show an...

Apart from the regular and adjugate compounds of a matrix, an inverse compound of a matrix is defined. Theorems of Laplace, Binet-Cauchy, and Jacobi are given in terms of these compounds. Compound matrices allow the statements of the theorems to be terse and precise

We consider the asymptotic spectral distribution of Hermitian Toeplitz matrices formally generated by a rational function , where deg() deg(), and are relatively prime, and the zeros of are in the open punctured disk . From Szegö's theorem, the eigenvalues of are distributed like the values of...

Limit spectral theory of sample covariance matrices of increasing dimension was recently used as a base for the development of improved non-degenerating methods of multivariate statistical analysis. We present results of a numerical investigation of fundamental relations of this theory (of the...

We study the matrices of in-forests of a weighted digraph Γ and their connections with the Laplaeian matrix of Γ. The () entry of is the total weight of spanning converging forests () with arcs such that belongs to a tree rooted at . The forest matrices, , can be calculated recursively and...