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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 paper, the authors review the properties of the Kronecker product of square matrices in terms of Hubbard operators and derive closed forms of the Clebsch-Gordan coefficients that rule the addition of angular momenta.
22 citations
TL;DR: In this paper, a unified spectral method for the analysis of regular matrix polynomials with non-zero determinant was proposed, which extends the above methods and results to the class of all regular matrix regular polynomial matrices.
Abstract: INTRODUCTION A spectral method for the analysis of monic matrix polynomials was developed recently in [8-10]. A similar method was developed [11-12] for non-monic, especially comonic, matrix polynomials. The present work suggests a unified approach, which extends the above methods and results to the class of all regular matrix polynomials (i.e. with non-zero determinant). The spectral method basically concerns the construction of a pair of matrices (X,T) , called a standard pair, from the spectral data of the given matrix polynomial A(I) , and is described in Sections 1-4. The inverse problem, namely the construction of A(1) from the pair (X,T] , is described in Section 5. In Section 6 we discuss a representation for A-l(1) and its application to basic linear systems of equations, and in Section 7, all factorizations of A(I) are characterized by certain restrictions on the pair (X,T) .
22 citations
TL;DR: In this paper, the nonnegativity of a square matrix A, its group inverse A # and its group projector AA # is used to define different sets for which relationships and characterizations are given.
22 citations
TL;DR: To speed up the computations, a new algorithm based on low-rank approximations of the matrix exponential is proposed and justified and it is proved that it computes γ(t) with a given accuracy.
Abstract: This work is devoted to computing the function γ(t)=∥exp(tA)∥2 in a given time interval 0≤t1≤t≤t2, where A is a square matrix whose eigenvalues have negative real parts. The main emphasis is put on computations of the maximal value of γ(t) for t≥0. To speed up the computations, we propose and justify a new algorithm based on low-rank approximations of the matrix exponential and prove that it computes γ(t) with a given accuracy. We discuss its implementation and demonstrate its efficiency with some numerical experiments.
22 citations
TL;DR: In this article, the exact computation of one point in each connected component of the real determinantal variety was studied, and the complexity of the problem was shown to be polynomial in the binomial coefficient.
22 citations