Showing papers on "Matrix analysis published in 1979"
Book•
01 Aug 1979
TL;DR: 1. Matrices which leave a cone invariant 2. Nonnegative matrices 3. Semigroups of non negative matrices 4. Symmetric nonnegativeMatrices 5. Generalized inverse- Positivity 6. M-matrices 7. Iterative methods for linear systems 8. Finite Markov Chains
Abstract: 1. Matrices which leave a cone invariant 2. Nonnegative matrices 3. Semigroups of nonnegative matrices 4. Symmetric nonnegative matrices 5. Generalized inverse- Positivity 6. M-matrices 7. Iterative methods for linear systems 8. Finite Markov Chains 9. Input-output analysis in economics 10. The Linear complementarity problem 11. Supplement 1979-1993 References Index.
6,572 citations
TL;DR: In this paper, the concept of displacement ranks is introduced to measure how close a given matrix is to Toeplitz matrices, and it is shown that these non-Toeplitzer matrices should be invertible with a complexity between O(N2 and O(3).
480 citations
TL;DR: By introducting a way of characterizing matrices in terms of their “distance” from being Toeplitz, a natural extension of recursive algorithms for finding the inverses of ToEplitz or displacement-type matrices is obtained.
220 citations
TL;DR: In this article, the dispersion matrix of balanced data in a two-way crossed-classification variance-components model is generalized to the case of any balanced-data variance component model, consisting of crossed and/or nested classifications.
Abstract: The dispersion matrix of balanced data in a two-way crossed-classification variance-components model is generalized to the case of any balanced-data variance-components model, consisting of crossed and/or nested classifications. The eigenvalues, determinant and inverse, of this generalized matrix are derived.
51 citations
TL;DR: In this paper, the authors studied the congruence relation between nonsingular symmetric and skew-symmetric matrices in the set of all real matrices A,B and showed that A and B are S-congruent if there is a nonsingul upper triangular matrix R such that A = RTBR.
42 citations
TL;DR: It is proved that within the class of P0-matrices, theQ-matrix are precisely the regular matrices.
Abstract: This paper concerns three classes of matrices that are relevant to the linear complementarity problem. We prove that within the class ofP
0-matrices, theQ-matrices are precisely the regular matrices.
31 citations
TL;DR: In this article, necessary and sufficient conditions for the eigenvalues of a complex matrix to lie in an algebraic region of the complex plane are given in terms of rational functions of the matrix coefficients, and are either by Kronecker product matrices or by positive definite matrices.
Abstract: Necessary and sufficient conditions are given for the eigenvalues of a complex matrix to lie in an algebraic region of the complex plane. These conditions are in terms of rational functions of the matrix coefficients, and are given either by Kronecker product matrices or by positive definite matrices. Finally, we remark on recent results concerning root clustering in a sector.
23 citations
TL;DR: In this article, it was proved that a 3×3 embeddable stochastic matrix has a representation as a product of a finite number of elementary stochastically matrices, with only one off-diagonal element positive.
Abstract: It is proved that a 3×3 embeddable stochastic matrix has a representation as a product of a finite number of elementary stochastic matrices, with only one off-diagonal element positive. In particular if the determinant is ≧1/2 then only 6 matrices are needed and a necessary and sufficient condition for embeddability in this case is given.
19 citations
TL;DR: In this paper, a class Σ of matrices is studied which contains, as special subclasses, p -circulant matrices (p ⩾ 1), Toeplitz symmetric matrices and the inverses of some special tridiagonal matrices.
16 citations
TL;DR: In this paper, a real-time matrix multiplication method for coherent optical astigmatic systems is presented, which is essentially composed of two subsystems that are connected in series, and the first one performs multiplications between the corresponding elements of the matrices coded in the amplitude transmittance of the transparencies.
Abstract: A method for real-time matrix multiplication is presented. This paper describes the geometrical interpretation of the mathematical manipulations between the two matrices. Three coherent optical astigmatic systems are developed based on the analysis. Each system is essentially composed of two subsystems that are connected in series. The first one performs multiplications between the corresponding elements of the matrices coded in the amplitude transmittance of the transparencies. The results are received by the second subsystem that performs the necessary summation operations to give the calculated rise to each element in the final result, the product of the two matrices. In these processes, no preparation of a hologram or intermediate memory is required. The operations are done in parallel. The multiplication between an N x N matrix and an N x 1 vector is discussed in detail. Multiplication between N x N and N x N matrices is also presented.
TL;DR: In this paper, the authors used a special distribution of random matrices as a model for estimating a priori the machine precision needed to solve large linear systems and showed that its matrices are almost never ill-conditioned.
Abstract: In 1946, von Neumann and his collaborators used a special distribution of random matrices as a model for estimatinga priori the machine precision needed to solve large linear systems. The present paper identifiesisotropy as a group-theoretic property of this distribution, shows that its matrices are almost never ill-conditioned, and explains how to use other isotropically distributed random matrices for testing the accuracy of numerical methods for solving linear systems and associated error diagnostics.
TL;DR: In this article, it was shown that every proper 2D transfer matrix is feedback equivalent to a separable proper transfer matrix, which is the case for all proper transfer matrices.
Abstract: In this note it is shown that every proper 2-D transfer matrix is feedback equivalent to a separable proper 2-D transfer matrix.
TL;DR: In this paper, a new class of elementary matrices is presented which are convenient in Jacobi-like diagonalization methods for arbitrary real matrices, and the presented transformations possess the norm-reducing property and produce an ultimate quadratic convergence.
Abstract: A new class of elementary matrices is presented which are convenient in Jacobi-like diagonalisation methods for arbitrary real matrices. It is shown that the presented transformations possess the normreducing property and that they produce an ultimate quadratic convergence even in the case of complex eigenvalues. Finally, a quadratically convergent Jacobi-like algorithm for real matrices with complex eigenvalues is presented.
TL;DR: In this paper, the authors studied useful criteria under which the quadratic forms x ∆ Ax and X ∆ Bx can vanish simultaneously and some real linear combination of A, B can be positive definite.
TL;DR: An iterative method of constructing projection matrices on the intersection of subspaces is considered, using a product of elementary matrices, and a convergence theorem with two natural assumptions about the gain sequence and the order of representations of the matrices is established.
Abstract: An iterative method of constructing projection matrices on the intersection of subspaces is considered, using a product of elementary matrices. A convergence theorem with two natural assumptions, concerning the gain sequence and the order of representations of the matrices, is established. The result has an application in forming associative memories.
01 Nov 1979
TL;DR: In this paper, integrating matrices are derived for arbitrarily spaced grid points using either interpolating or least squares fit orthogonal polynomials, and several features of the equally spaced grid case are discussed.
Abstract: Integrating matrices are derived for arbitrarily spaced grid points using either interpolating or least squares fit orthogonal polynomials. Several features of the equally spaced grid case are also discussed.
TL;DR: In this article, an efficient formula for determining the matrix of frequency response functions is derived for the linear system of ordinary differential equations of structural dynamics having constant coefficients, and the eigenvalues and eigenvectors of the system associated with the known mass, stiffness and damping matrices are used to accomplish this without recourse to the inversion of complex matrices at each excitation frequency.
TL;DR: In this paper, a diagonal matrix D ∗ was found to minimize an upper bound on the spectral condition number of the nonsingular matrix DA, and the resulting linear system GAx=Gc is expected to be more suitable than Ax=c for numerical solution by the conjugate gradient and other methods.
01 Jan 1979
TL;DR: Motivation for the choice of order of elimination in dealing with sparse symmetric matrices is provided by consideration of a network analogue and then generalized to asymmetricMatrices.
Abstract: Motivation for the choice of order of elimination in dealing with sparse symmetric matrices is provided by consideration of a network analogue and then generalized to asymmetric matrices.
01 Dec 1979
TL;DR: In this article, a method for the design of Luenberger observers for linear systems is developed utilizing generalized inverses of matrices, which can be applied both to time-invariant and time-varying systems.
Abstract: A method for the design of Luenberger observers for linear systems is developed utilizing generalized inverses of matrices The method can be applied both to time-invariant and to time-varying systems
TL;DR: The group-theoretic complexity of many subsemigroups of the semigroup B n of n × n Boolean matrices, including Hall matrices and reflexive matrices was studied in this article.