Topic
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: The inner-outer factorization for square real rational matrices which may have zeros on the jω-axis including infinity is discussed and a factorization method is given in terms of the descriptor form representation of the rational matrix.
45 citations
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TL;DR: In this paper, a finitely computable graph-theoretic answer is given to the following question concerning linear dynamical systems: When, given only the signs of entries (+, -, or 0) in a real square matrix A, can one be certain that all positive trajectories of the system ẋ = Ax are bounded?
44 citations
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TL;DR: In this article, a numerical method for computing Fisher information matrix about the five parameters of a mixture of two normal distributions is presented, by using a simple transformation which reduces the number of parameters from five to three.
Abstract: This paper presents a numerical method for computation of the Fisher information matrix about the five parameters of a mixture of two normal distributions. It is shown, by using a simple transformation which reduces the number of parameters from five to three, that the computation of the whole information matrix leads to the numerical evaluation of a particular integral. The Hermite-Gauss quadrature formula, Romberg's algorithm, a power series, and Taylor's expansion are applied for the evaluation of this integral and the results are compared with each other. A short table has been provided from which the approximate information matrix can be obtained in practice.
44 citations
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15 Mar 2005TL;DR: In this paper, a matrix (I) of eigenvectors is derived using an iterative procedure, where an eigenmode matrix Vi is first initialized, e.g., to an identity matrix, and then updated based on a channel response matrix (II) for a MIMO channel to obtain an updated eigen mode matrix Vi+1.
Abstract: A matrix (I) of eigenvectors is derived using an iterative procedure. For the procedure, an eigenmode matrix Vi is first initialized, e.g., to an identity matrix. The eigenmode matrix Vi is then updated based on a channel response matrix (II) for a MIMO channel to obtain an updated eigenmode matrix Vi+1. The eigenmode matrix may be updated for a fixed or variable number of iterations. The columns of the updated eigenmode matrix may be orthogonalized periodically to improve performance and ensure stability of the iterative procedure. In one embodiment, after completion of all iterations, the updated eigenmode matrix for the last iteration is provided as the matrix (III).
44 citations
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29 Jul 2010
TL;DR: In this article, the minimum dwell time of switched linear systems was investigated by exploiting homogeneous polynomial Lyapunov functions and convex optimization problems based on linear matrix inequalities (LMIs).
Abstract: This paper investigates the minimum dwell time for switched linear systems. It is shown that a sequence of upper bounds of the minimum dwell time can be computed by exploiting homogeneous polynomial Lyapunov functions and convex optimization problems based on linear matrix inequalities (LMIs). This sequence is obtained by adopting two possible representations of homogeneous polynomials, one based on Kronecker products, and the other on the square matrix representation (SMR). Some examples illustrate the use and the potentialities of the proposed approach. It is also conjectured that the proposed approach is asymptotically nonconservative, i.e. the exact minimum dwell time is obtained by using homogeneous polynomials with sufficiently large degree.
44 citations