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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: Some theorems concerning the application of the e-algorithm to vectors satisfying a matrix difference equation are proved and generalize results on the scalar e-Algorithm and some recent theorem on the vector e- algorithm.
26 citations
TL;DR: A survey of matrix means and matrix inequalities is presented with the work of Ando, Anderson and Duffin being showcased in this paper, where the classical Arithmetic-Geometric-Harmonic Mean for two Hermitian positive semidefinite matrices is given.
Abstract: A survey of matrix means and matrix inequalities is presented with the work of Ando, Anderson and Duffin being showcased. The classical Arithmetic-Geometric-Harmonic Mean for two Hermitian positive semidefinite matrices is given. Other classical means such as the Gaussian Mean, power means and the symmetric function means are also discussed.
26 citations
TL;DR: In this paper, the maximum eigenvalues of the reciprocal distance matrix and the reverse Wiener matrix of a connected graph were investigated and the Nordhaus-Gaddum-type results for them were obtained.
Abstract: We report some properties of the maximum eigenvalues of the reciprocal distance matrix and the reverse Wiener matrix of a connected graph, in particular, various lower and upper bounds, and the Nordhaus–Gaddum-type results for them. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008
25 citations
TL;DR: In this paper, the consequences of arbitrary changes of the final demand vector for the gross production vector in the open Leontief model are studied, and several properties of non-negative irreducible square matrices are obtained.
25 citations
TL;DR: It is shown that for any monic linearization $\lambda I+A$ of an $n\times n$ quadratic matrix polynomial there exists a nonsingular matrix defined in terms of $n$ orthonormal vectors that transforms $A$ to a companion linearization of a (quasi-)triangular quadratics matrix poynomial.
Abstract: We show that any regular quadratic matrix polynomial can be reduced to an upper triangular quadratic matrix polynomial over the complex numbers preserving the finite and infinite elementary divisors. We characterize the real quadratic matrix polynomials that are triangularizable over the real numbers and show that those that are not triangularizable are quasi-triangularizable with diagonal blocks of sizes $1\times 1$ and $2 \times 2$. We also derive complex and real Schur-like theorems for linearizations of quadratic matrix polynomials with nonsingular leading coefficients. In particular, we show that for any monic linearization $\lambda I+A$ of an $n\times n$ quadratic matrix polynomial there exists a nonsingular matrix defined in terms of $n$ orthonormal vectors that transforms $A$ to a companion linearization of a (quasi-)triangular quadratic matrix polynomial. This provides the foundation for designing numerical algorithms for the reduction of quadratic matrix polynomials to upper (quasi-)triangular form.
25 citations