Showing papers on "Square matrix published in 1990"
TL;DR: In this article, a simple and accurate extended Jones matrix representation for the twisted nematic liquid crystal display at the oblique incidence was obtained for the first time, which is quite close to those obtained by the faster 4×4 matrix method with spectrum averaging to account for the nonzero bandwidth of the incident light.
Abstract: A simple and accurate extended Jones matrix representation for the twisted nematic liquid‐crystal display at the oblique incidence was obtained for the first time. The results obtained by this extended Jones matrix representation are quite close to those obtained by the faster 4×4 matrix method with spectrum averaging to account for the nonzero bandwidth of the incident light. However, the computation time for the extended Jones matrix method is less than half that of the faster 4×4 matrix method without spectrum averaging. Furthermore, at normal incidence, this extended Jones matrix representation reduces to the ordinary Jones matrix representation.
317 citations
TL;DR: A method is presented based on combinatorial considerations which permutes the rows and columns of a general matrix in such a way that relatively dense blocks of various sizes appear along the diagonal.
Abstract: Block iterative methods used for the solution of linear systems of algebraic equations can perform better when the diagonal blocks of the corresponding matrix are carefully chosen. A method is presented based on combinatorial considerations which permutes the rows and columns of a general matrix in such a way that relatively dense blocks of various sizes appear along the diagonal. The method is particularly useful when no natural partitioning of the matrix is available. Two parameters govern the method which is $O(n +
u )$ in time and space, where n is the order of the matrix and $
u $ is the number of nonzeros in the matrix. Numerical test results are presented which illustrate the performance of both the ordering algorithm and the block iterative methods with the resulting orderings.
55 citations
TL;DR: An O((m + n)3) algorithm for deciding total unimodularity of any real m × n matrix, i.e., for deciding whether or not every square submatrix of the given matrix has determinant 0 or ±1.5.
51 citations
TL;DR: In this article, it was shown that any complex square matrix T is a sum of finitely many idempotent matrices if and only if trT is an integer and trT ⩾ rank T. The problem of the minimum number of idempots needed to sum T and obtain some partial results.
36 citations
36 citations
TL;DR: The invariant subspace theorem of Brown, Chevreau and Pearcy as discussed by the authors states that every contraction on a Hubert space whose spectrum contains the unit circle has nontrivial invariants.
Abstract: The main purpose of this article is to give an approach to the recent invariant subspace theorem of Brown, Chevreau and Pearcy: Every contraction on a Hubert space, whose spectrum contains the unit circle has nontrivial invariant subspaces. Our proof incorporates several of the recent ideas tying together function theory and operator theory. 1. I N T R O D U C T I O N The Jordan structure theorem for finite matrices has been known now for over one hundred years, and its usefulness can hardly be overstated. It says that every square matrix A over the complex numbers C is similar to another matrix B (i.e., B = XAX~ for some invertible matrix X) which is a direct sum of Jordan cells. That is, B can be written in block form \BX 0 ••• 0 ] B=\° * '" ° [o 0 ... Bk\ and each Bt has the form [A, 0 0
35 citations
TL;DR: In this paper, the rank conditions on g-inverses of A, M and L of orders n × m, n × q and m × r respectively were studied, and the L -inverse, M-inverse and LMN inverse matrices were shown to be idempotent under rank conditions.
33 citations
TL;DR: In this article, it was shown that the result does not hold if X is permitted to be a general square matrix and a counterexample is supplied for noncommuting matrices.
Abstract: A short and direct proof of the convexity property is given. It is shown that the theorem applies to any convex, commuting set of matrices in R/sup nXn/, where A/sub 0/ in R/sup nXn/ is fixed. It is also shown that the result does not hold if X is permitted to be a general square matrix. A counterexample is supplied for noncommuting matrices. >
27 citations
TL;DR: An O(n4) algorithm for checking whether the rows and columns of a given matrix can be permuted in such a way that the obtained matrix has the Monge property is presented.
21 citations
TL;DR: The notion of Bezoutian of nonsquare matrix polynomials is defined in this paper, and a generalization of the Gohberg-Semencul formula for the inverse of a generalized Toeplitz matrix is proved.
20 citations
TL;DR: In this article, the response of non-conservative linear systems without any particular assumption about the nature of the matrix coefficients, multiplicity of eigenvalues or external forcing is determined in terms of the dynamical matrix solution of the given system.
TL;DR: In this paper, a necessary and sufficient condition for strong regularity was proved, together with an O(n 2 log n )-time method for testing this property, where n is the number of nodes in the input space.
TL;DR: In this article, a complete solution to the system of differential equations ∇f = M∇g, where M is a given square matrix, is presented. But this solution is not suitable for the case of constant matrices.
Abstract: The system of differential equations ∇f = M∇g, where M is a given square matrix, arises in many contexts. A complete solution to this problem in the case when M is a constant matrix is presented here. Applications to continuum mechanics and biHamiltonian systems are indicated.
TL;DR: The scalar matrix formulation allows for the use of a standard Gaussian elimination to reduce the matrix to diagonal form or for reduction to upper triangular form together with back substitution, which result in significant reductions in computing time.
TL;DR: In this article, a symmetric difference scheme for linear, stiff, or singularly perturbed boundary value problems of first order with constant coefficients is constructed, being based on a stability function containing a matrix square root.
Abstract: A symmetric difference scheme for linear, stiff, or singularly perturbed boundary value problems of first order with constant coefficients is constructed, being based on a stability function containing a matrix square root. Its essential feature is the unconditional stability in the absence of purely imaginary eigenvalues of the coefficient matrix. Local damping of errors, uniform stability, and uniform second-order convergence are proved. The computation of the specific matrix square root by a well-known, stable variant of Newton’s method is discussed. A numerical example confirming the results is given.
TL;DR: In this paper, the authors consider the problem of the factorization of polynomial matrices over an arbitrary field in connection with their reducibility by semiscalar equivalent transformations to triangular form with the invariant factors along the principal diagonal.
Abstract: One considers the problem of the factorization of polynomial matrices over an arbitrary field in connection with their reducibility by semiscalar equivalent transformations to triangular form with the invariant factors along the principal diagonal. In particular, one establishes a criterion for the representability of a polynomial matrix in the form of a product of factors (the first of which is unital), the product of the canonical diagonal forms of which is equal to the canonical diagonal form of the given matrix. There is given also a method for the construction of such factorizations.
TL;DR: The method presented for the synthesis of 2-D multiports is based mainly on a paraunitary bordering of the given scattering matrix of the desired network in order to obtain the scattering Matrix of alossless 2- D multiport, which can be realized by using known procedures.
Abstract: Two-dimensional (2-D) passive networks are of interest e.g. for use as reference filters for two-dimensional wave digital filters. Necessary properties of the impedance matrix and scattering matrix, respectively, of such n-ports have been established, but not yet been shown to be also sufficient for a given two-variable rational matrix to be the impedance matrix or scattering matrix, respectively, of a passive network containing lumped elements. In the design of 2-D passive n-ports it will be however of great interest whether this mentioned feature can be used as a basis for ageneral synthesis procedure. In this paper it is shown that this is the case. The method presented for the synthesis of 2-D multiports is based mainly on a paraunitary bordering of the given scattering matrix of the desired network in order to obtain the scattering matrix of alossless 2-D multiport, which can be realized by using known procedures. The socalled spectral factorization of a two-variable para-Hermitian polynomial matrix which is nonnegative definite forp =j
w plays a crucial role in the design approach presented. No restrictions are made concerning the coefficients of the given rational scattering matrix; they may be either real or complex, so as to include even complex networks which are of special interest for multidimensional systems.
01 Oct 1990
TL;DR: The Hermitian test matrix is obtained as the inverse of the Gram matrix of a natural basis in a certain Krein space of rational vector functions associated with a polynomial.
Abstract: Let N(λ) be a square matrix polynomial, and suppose det N is a polynomial of degree d. Subject to a certain non-singularity condition we construct a d by d Hermitian matrix whose signature determines the numbers of zeros of N inside and outside the unit circle. The result generalises a well known theorem of Schur and Cohn for scalar polynomials. The Hermitian “test matrix” is obtained as the inverse of the Gram matrix of a natural basis in a certain Krein space of rational vector functions associated with N. More complete results in a somewhat different formulation have been obtained by Lerer and Tismenetsky by other methods.
TL;DR: In this paper, an explicit Hermitian canonical form for complex square matrices under consimilarity has been proposed, which is based on a simple algorithmic procedure to construct a concanonical form that is not only canonical but also hermitian.
TL;DR: An algorithm to assign an arbitrary normalized Hessenberg matrix that seems to be computationally more effective than the former and can be used to assign most of the important canonical forms above and a given set of eigenvalues as well.
TL;DR: In this article, a characterization of semiproper matrix functions in terms of proper matrix functions is presented, and a new and systematic procedure for decomposing a semi-probability matrix function into a finite sum of mutually commutative proper ones is presented.
TL;DR: In this paper, the critical behavior of large-N matrix models with potentials of the form V(M) = ΣkN1−kgktr(M2k) was studied.
Abstract: We study the critical behavior in D = 1 large-N matrix models with potentials of the form V(M) = ΣkN1−kgktr(M2k) for hermitian matrices, and also those of the form for the unitary matrices. For the planar theory, both cases show multicritical points characterized by an integer m ≥ 2 with and . We also look at the subleading terms in susceptibility in order to find out the dimensions of some of the operators in the theory. The question of identification for m > 2, however, remains unsettled.
23 May 1990
TL;DR: In this paper, the robustness of the design of a Sendzimir cold rolling mill is analyzed in terms of a set of strict inequalities, with respect to errors in the transfer function matrix.
Abstract: The shape control problem, for a Sendzimir Cold Rolling Mill, is multivariable. The plant transfer function matrix, has the special form: G(s) = g(s)G m , where g(s) is a scalar transfer function and G m a square matrix of constant gains. G m , however, is not invertible, but the system is diagonalised using an eigenvector/eigenvalue decomposition resulting in a scalar frequency response design problem. An important consideration in shape control systems is the robustness of the design due to the wide range of materials rolled, reflected in changes in the elements of G m . To this end, a development is included which represents the robustness of the design, with respect to errors in G m , in terms of a set of strict inequalities.
TL;DR: In this article, the first and second moments of a matrix quadratic form under normality assumptions are derived and then differentiated using a matrix differential calculus (MDC) under the assumption of normality.
Abstract: In order to obtain the first and second moments of a matrix quadratic form under normality assumptions its moment generating function will be derived and then differentiated. Use is being made of matrix differential calculus as developed by the author
TL;DR: In this article, the Hungarian algorithm is applied to the traveling salesman problem and the Hungarian form of A = [aij] is obtained in polynomial time for all Hungarian forms associated with A. The original matrix A and its triangular block form have the same set of optimal tours, up to a renumbering of the cities.
TL;DR: In this article, a computational improvement on an algorithm previously derived for the natural log of a square matrix is presented, allowing a more general use of the algorithm, useful in estimating the state-space model of a continuous-time multivariable system from data obtained with a discrete-time model.
Abstract: A computational improvement on an algorithm previously derived for the calculation of the natural log of a square matrix is presented, allowing a more general use of the algorithm. This algorithm is useful in estimating the state-space model of a continuous-time multivariable system from data obtained with a discrete-time model.
TL;DR: The use of component matrices in linear time-invariant dynamic models of bioscience systems is demonstrated and a new recursive method to find these componentMatrices is developed.
Abstract: Component matrices of a given square matrix can be used for a variety of purposes. A new recursive method to find these component matrices is developed. The use of component matrices in linear time-invariant dynamic models of bioscience systems is demonstrated.
TL;DR: In this article, it was shown that a given square matrix can be decomposed into a particular combination of circulant matrices, each in cascade with a modulator, which can be interpreted as a decomposition of a linear discrete-time time-invariant system.
Abstract: It is shown that a given square matrix can be decomposed into a particular combination of circulant matrices. From a linear system viewpoint, the above result can be interpreted as a decomposition of a linear discrete-time time-invariant system into a particular combination of linear discrete-time time-invariant systems, each in cascade with a modulator. >
TL;DR: In this article, the minimum dimension for a square matrix of order is defined and the minimum dimensions of the square matrix can be computed using Euclidean distance metric (MDSM).
Abstract: (1990). Minimum Dimension for a Square Matrix of Order n. The College Mathematics Journal: Vol. 21, No. 1, pp. 28-34.