Hamiltonian matrices with respect to a nondegenerate skewsymmetric or skewhermitian indefinite inner product in finite dimensional real, complex, or quaternion vector spaces are studied. Subspaces that are simultaneously invariant for the matrices and neutral in the indefinite inner product are of special interest. The dimension of maximal (by inclusion) such subspaces is identified in terms of...

We give new examples and describe the complete lists of all measures on the set of countable homogeneous universal graphs and Ksfree homogeneous universal graphs (for s ≥ 3) that are invariant with respect to the group of all permutations of the vertices. Such measures can be regarded as random graphs (respectively, random Ks-free graphs). The well-known example of Erdös–Rényi (ER) of the rando...

In this paper we present a new, compact derivation of state-space formulae for the so-called discretisation-based solution of the H 1 sampled-data control problem. Our approach is based on the established technique of continuous time-lifting, which is used to isometri-cally map the continuous-time, linear, periodically time-varying, sampled-data problem to a discrete-time, linear, time-invarian...

This paper provides a solution to the problem of computing a robustly positively invariant outer approximation of the minimal robustly positively invariant set for a discretetime, linear, time-invariant system. It is assumed that the disturbance is additive and persistent, but bounded.

Matrix equations (AX = B,XC = D) is a class of important matrix equations. The problem of the solution of the matrix equations (AX = B,XC = D) arise in engineering and in some special matrix inverse problems [1-3]. Many authors have been devoted to the study of this problem, and a series of useful results have been obtained. For example, Mitra [4] gave the common solution of minimum possible ra...

A bistochastic matrix B of size N is called unistochastic if there exists a unitary U such that Bij = Uij 2 for i , j=1, . . . ,N. The set U3 of all unistochastic matrices of order N=3 forms a proper subset of the Birkhoff polytope, which contains all bistochastic doubly stochastic matrices. We compute the volume of the set U3 with respect to the flat Lebesgue measure and analytically evaluate ...

A new algebraic framework is introduced based on stochastic matrices. Together with several new operators, the set of stochastic matrices is shown to constitute a vector space, an inner-product space, and an associative algebra. The new zero vector is the uniform probability distribution and linear addition is akin to statistical independence. This new stochastic algebra allows Markov chains an...

Given a square matrix A, the inverse subspace problem is concerned with determining a closest matrix to A with a prescribed invariant subspace. When A is Hermitian, the closest matrix may be required to be Hermitian. We measure distance in the Frobenius norm and discuss applications to Krylov subspace methods for the solution of large-scale linear systems of equations and eigenvalue problems as...

We introduce and study a 2–parameter family of unitarily invariant probability measures on the space of infinite Hermitian matrices. We show that the decomposition of a measure from this family on ergodic components is described by a determinantal point process on the real line. The correlation kernel for this process is explicitly computed. At certain values of parameters the kernel turns into...

A real square matrix satisfies the weak Hawkins-Simon condition if its leading principal minors are positive (the condition was first studied by the French mathematician Maurice Potron). Three characterizations are given. Simple sufficient conditions ensure that the condition holds after a suitable reordering of columns. A full characterization of this set of matrices should take into account t...