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Square matrix
About: Square matrix is a research topic. Over the lifetime, 5000 publications have been published within this topic receiving 92428 citations.
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TL;DR: In this article, the generalized second-order Sylvester matrix equation is solved using a parametric solution, where the matrix F does not need to be in any canonical form, or may even be unknown a priori.
Abstract: This note provides a complete general parametric solution (V,W) to the generalized second-order Sylvester matrix equation MVF/sup 2/+DVF+KV=BW, with F being an arbitrary square matrix. The primary feature of this solution is that the matrix F does not need to be in any canonical form, or may be even unknown a priori. The results provide great convenience to the computation and analysis of the solutions to this class of equations, and can perform important functions in many analysis and design problems involving second-order dynamical systems.
67 citations
TL;DR: In this paper, a representation for nonnegative definite matrix polynomials is obtained, which is used to characterize moment points by properties of generalized Hankel matrices, and an explicit representation of the orthogonal polynomial with respect to a given matrix measure is derived.
66 citations
TL;DR: In this paper, the integrable systems that arise in the continuum theory are shown to result directly from the formulation of the matrix integrals in terms of orthogonal polynomials.
Abstract: The matrix integrals involved in 2d lattice gravity are studied at finiteN. The integrable systems that arise in the continuum theory are shown to result directly from the formulation of the matrix integrals in terms of orthogonal polynomials. The partition function proves to be a tau function of the Toda lattice hierarchy. The associated linear problem is equivalent to finding the polynomial basis which diagonalizes the partition function. The cases of one Hermitian matrix, one unitary matrix, and Hermitian matrix chains all fall within the Toda framework.
66 citations
TL;DR: In this paper, the nonlinear matrix equation X + A*X(-1)A = P, where A, P are n x n complex matrices with P Hermitian positive definite, and A* denotes the conjugate transpose of a matrix A.
66 citations
TL;DR: The inverse interval matrix as mentioned in this paper is defined as the narrowest interval matrix containing the inverses of all the matrices from a given interval matrix, and it is the smallest interval matrix that can be computed in polynomial time.
Abstract: The inverse interval matrix is defined as the narrowest interval matrix containing the inverses of all the matrices from a given interval matrix. Both theoretical and practical results concerning computation of the inverse interval matrix are presented. In particular, explicit formulas are given for the inverse of an interval matrix with radius of rank one.
66 citations