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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, a matrix generalization of the inverse scattering method is developed to solve the multicomponent nonlinear Schrodinger equation with nonvanishing boundary conditions, and it is shown that the initial value problem can be solved exactly.
Abstract: Matrix generalization of the inverse scattering method is developed to solve the multicomponent nonlinear Schrodinger equation with nonvanishing boundary conditions. It is shown that the initial value problem can be solved exactly. The multi-soliton solution is obtained from the Gel’fand-Levitan-Marchenko [Amer. Math. Soc. Transl. 1, 253 (1955)] equation.
46 citations
TL;DR: A conference matrix of order n is a square matrix C with zeros on the diagonal and ± 1 elsewhere, which satisfies the orthogonality condition CCT = (n − 1)I as mentioned in this paper.
Abstract: A conference matrix of order n is a square matrix C with zeros on the diagonal and ±1 elsewhere, which satisfies the orthogonality condition CCT = (n — 1)I. If in addition C is symmetric, C = CT, then its order n is congruent to 2 modulo 4 (see [5]). Symmetric conference matrices (C) are related to several important combinatorial configurations such as regular two-graphs, equiangular lines, Hadamard matrices and balanced incomplete block designs [1; 5; and 7, pp. 293-400]. We shall require several definitions.
45 citations
TL;DR: A condition which is necessary and sufficient for the strong linear independence of columns of a given matrix in the minimax algebra based on a dense linearly ordered commutative group and a connection with the classical assignment problem is formulated.
45 citations
04 Dec 2001
TL;DR: In this article, Hsu et al. extended the model-reference adaptive control (MRAC) for more general plants with relative degree greater than one and presented three possible factorizations of K/sub p/ and the resulting update laws.
Abstract: A MIMO (multiple-input, multiple-output) analog to the well-known Lyapunov-based SISO (single-input, single-output) design of MRAC (model-reference adaptive control) has been recently introduced by L. Hsu et al. (2001). The new design utilizes a control parametrization derived from a factorization of the high-frequency gain matrix K/sub p/=SDU, where S is symmetric positive-definite, D is diagonal and U is unity upper-triangular. Only the signs of the entries of D or, equivalently, the signs of the leading principal minors of K/sub p/, were assumed to be known. However, the result was restricted to plants with (vector) relative degree one. In this paper, we extend the MRAC for more general plants with relative degree greater than one. We present three possible factorizations of K/sub p/ and the resulting update laws.
45 citations
TL;DR: In this article, bounds on the variance of a finite universe were derived for the roots of the polynomial equations and bounds for the largest and smallest eigenvalues of a square matrix with real spectrum.
Abstract: We derive bounds on the variance of a finite universe. Some related inequalities for the roots of the polynomial equations and bounds for the largest and smallest eigenvalues of a square matrix with real spectrum are obtained.
45 citations