Related papers: Linear matrix equations with parameters forming a …
A hermitian matrix can be parametrized by a set consisting of its determinant and the eigenvalues of its submatrices. We established a group of equations which connect these variables with the mixing parameters of diagonalization. These…
A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…
We prove that the algebraic set of pairs of matrices with a diagonal commutator over a field of positive prime characteristic, its irreducible components, and their intersection are $F$-pure when the size of matrices is equal to 3.…
Multivariate process satisfying affine stochastic recurrence equation with generic diagonal matrices is considered. We prove that the stationary solution is regularly varying. The results are applicable to diagonal autoregressive models.
We provide a solution to the problem of simultaneous $diagonalization$ $via$ $congruence$ of a given set of $m$ complex symmetric $n\times n$ matrices $\{A_{1},\ldots,A_{m}\}$, by showing that it can be reduced to a possibly…
In this paper we study algebraic sets of pairs of matrices defined by the vanishing of either the diagonal of their commutator matrix or its anti-diagonal. We find a system of parameters for the coordinate rings of these two sets and their…
The analysis of diagonalizable matrices in terms of their so-called isospectral reduction represents a versatile approach to the underlying eigenvalue problem. Starting from a symmetry of the isospectral reduction, we show in the present…
Subsets of a matrix algebra over a field that are invariant under conjugation and contain the linear span of each two of their commuting elements are described. They obviously include the subsets of diagonalizable and nilpotent matrices. In…
We present a novel class of real symmetric matrices in arbitrary dimension $d$, linearly dependent on a parameter $x$. The matrix elements satisfy a set of nontrivial constraints that arise from asking for commutation of pairs of such…
In a recent article, we gave a full characterization of matrices that can be decomposed as a linear combination of two idempotents with prescribed coefficients. In this one, we use those results to improve on a recent theorem of V.…
We consider the (symmetric) Pascal matrix, in its finite and infinite versions, and prove the existence of symmetric tridiagonal matrices commuting with it by giving explicit expressions for these commuting matrices. This is achieved by…
Diagonally dominant matrices have many applications in systems and control theory. Linear dynamical systems with scaled diagonally dominant drift matrices, which include stable positive systems, allow for scalable stability analysis. For…
We study a nonlinear decomposition of a positive definite matrix into two components: the inverse of another positive definite matrix and a symmetric matrix constrained to lie in a prescribed linear subspace. Equivalently, the inverse…
It is well known that a set of non-defect matrices can be simultaneously diagonalized if and only if the matrices commute. In the case of non-commuting matrices, the best that can be achieved is simultaneous block diagonalization. Here we…
Using a recent result of Bogdanov and Guterman on the linear preservers of pairs of simultaneously diagonalizable matrices, we determine all the automorphisms of the vector space M_n(R) which stabilize the set of diagonalizable matrices. To…
Parametric linear systems are linear systems of equations in which some symbolic parameters, that is, symbols that are not considered to be candidates for elimination or solution in the course of analyzing the problem, appear in the…
The (matricial) solution set of a Linear Matrix Inequality (LMI) is a convex basic non-commutative semi-algebraic set. The main theorem of this paper is a converse, a result which has implications for both semidefinite programming and…
We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on…
In this paper we discuss a general algebraic approach to treating static equations of matrix models with a mass-like term. In this approach the equations of motions are considered as consequence of parafermi-like trilinear commutation…
This work presents closed formulas for determinant, permanent, inverse, and Drazin inverse of circulant matrices with two non-zero coefficients.