A basic decomposition result related to the notion of the rank of a matrix and applications.
A Brauer’s theorem and related results
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 classification of the nilpotent triangular matrices
A classification of two-peak sincere posets of finite prinjective type and their sincere prinjective representations
Assume that K is an arbitrary field. Let (I, ⪯) be a two-peak poset of finite prinjective type and let KI be the incidence algebra of I. We study sincere posets I and sincere prinjective modules over KI. The complete set of all sincere two-peak posets of finite prinjective type is given in Theorem 3.1. Moreover, for each such poset I, a complete set of representatives of isomorphism classes of sincere indecomposable prinjective modules over KI is presented in Tables 8.1.
A direct transformation between two fundamental matrix canonical forms
A formula for angles between subspaces of inner product spaces.
A local form for the automorphisms of the spectral unit ball.
A new family of companion forms of polynomial matrices.
A note on classes of structured matrices with elliptical type numerical range
We identify new classes of structured matrices whose numerical range is of the elliptical type, that is, an elliptical disk or the convex hull of elliptical disks.
A note on indecomposability of Boolean matrices
A pointwise approximation of isolated trees in a random graph.
A rational canonical form algorithm
We present an easy-to-implement algorithm for transforming a matrix to rational canonical form.
A rational canonical form for matrix fields
A remark on the canonical form for a pair of orthoprojectors.
A simple proof of the classification of normal Toeplitz matrices.
A structured staircase algorithm for skew-symmetric/symmetric pencils.
AB-Algorithm and Its Modifications for the Spectral Problems of Linear Pencils of Matrices.
Absolutely flat idempotents.
Additive decomposition of matrices under rank conditions and zero pattern constraints
This paper deals with additive decompositions of a given matrix , where the ranks of the summands are prescribed and meet certain zero pattern requirements. The latter are formulated in terms of directed bipartite graphs.
Algebraic matrix equations in systems theory