Showing papers in "Linear Algebra and its Applications in 1974"

TL;DR: In this paper, the Schur complement can be used in numerical linear algebra (NLAs) and the author is concerned with some of the ways in which it can be applied.

TL;DR: In this paper, necessary and sufficient conditions for n real numbers to be eigenvalues of an n × n nonnegative (or alternatively, positive) symmetric matrix and 2n real numbers for being eigen values and diagonal entries of a nonnegative symmetric matrices were given.

TL;DR: In this paper, the spectral inverse of a Toeplitz matrix A whose form is related to that of a circulant matrix is studied by describing the algebraic structure of the semigroup of all matrices commuting with a given matrix with distinct eigenvalues.

TL;DR: In this paper, the rank of the controllability matrix of A and W is used to derive a new inertia theorem for damping problems of the equation M x + (D + G) xdot; + Kx = 0.

TL;DR: The definition of a projector under a semileast square inverse of a complex matrix is given in this article, where the same concept can also be defined in terms of projectors under seminorms.

TL;DR: In this article, it was shown that the range of Φ is exactly the set of all invertible operators T for which T−1 is similar to T∗.

TL;DR: In this paper, an iterative method is described which rapidly computes the norm of a nonnegative matrix A, considered as a mapping from the finite dimensional space l r(n) to the space l p(m).

TL;DR: This paper showed that the Moore-Penrose inverse of AB can always be expressed as B−A− for some generalized inverse A− of A and B− of B. Some of the proofs are based on conditions for a product of projectors to be a projector.

TL;DR: Schneider-Vidyasagar et al. as discussed by the authors showed that the connections between A quasimonotone and exp( tA ) monotone are special cases of differential inequalities for initial value problems in partially ordered topological vector spaces.

TL;DR: In this paper, the authors characterized all n x n matrices whose spectral radius equals their spectral norm and showed that for n ⩾3 the class of these matrices contains the normal matrices as a subclass.

TL;DR: In this paper, a new lower bound for the Perron root ω of an irreducible nonnegative matrix A is obtained, where ω is greater than the sum of the greatest element of A plus the arithmetic mean of the two smallest main diagonal elements.

TL;DR: A brief survey of recent results on combinatorially symmetric matrices can be found in this paper, where a simple proof of a theorem of Parker and Youngs is presented.

TL;DR: For the eigenvalues λi of an n × n matrix A the inequality ∑ i |λ i | 2 (A 4 − 1 2 ‖D 2 ) 1 2 is proved, where D ≔ AA ∗ − A ∗ A and ‖ ● ‖; denotes the euclidean norm.

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.

TL;DR: A Lyapunov transformation is a linear transformation on the set H n of hermitian matrices H ϵ C n,n of the form L A(H) = A∗H + HA, where H is positive definite as mentioned in this paper.

TL;DR: For a square complex matrix A with positive definite imaginary component (A − A ∗ )⧸ 2 i, this paper studied Hermitian congruence, distribution of the eigenvalues {αj} of A − 1 A − ∗ relative to a line in the complex plane, variational properties of the arguments, real parts and imaginary parts of {aj}, and inequalities for determinants and singular values.

TL;DR: In this paper, some results were obtained relating topological properties of polyhedral cones to algebraic properties of matrices whose columns are the extremal vectors of the cone. And several characterizations of positive operators on polyhedral cone are given.

TL;DR: In this paper, the determinantal values for submatrices of two-commodity transportation problems (in terms of the number of disjoint capacitated routes) were established.

TL;DR: It is shown that if a linear transformation T on the space of n × n complex matrices maps non negative matrices into nonnegative matrices and preserves the spectrum of each nonnegative matrix, then T ( A) = P −1 AP or T (A) = T −1 A T P for all matrices A and a fixed nonnegative generalized permutation matrix P.

TL;DR: In this article, it was shown that a bounded multiplicative group of complex (real) n × n nonsingular matrices is similar to a unitary (orthogonal) group.

TL;DR: A necessary and sufficient condition for the existence of unitary matrices U and V such that UAV is a real diagonal matrix for every matrix A in some set Γ of rectangular complex matrices is given in this article.

TL;DR: In this article, it was shown that if S is a family of n×n normal matrices, and As is the algebra generated by S over the complex field, then the matrices in S are simultaneously unitarily similar to quasi-diagonal matrices if and only if (AB − BA)2Q = Q(AB −BA)2 for all A and B ∈ As, Q ∈ S. In fact, the domain of B can be further restricted.

TL;DR: In this paper, the authors investigated the numerical properties of the maximum and minimum diagonal sums of the matrices in the convex polyhedron of all n × n doubly stochastic (d.s.) matrices.

TL;DR: In this article, the spectral properties of an integral operator with a nonnegative continous kernel are investigated. But the authors focus on the spectral radius of the integral operator and do not consider the distribution of secondary eigenvalues.

TL;DR: In this paper, some new theorems are presented on the isolation effect in Hermitian matrices and the results are of importance in the computation of eigenvalues, particularly for tridiagonal matrices.

TL;DR: In this article, the authors present conditions which are necessary and sufficient for (AB >) + = B + A ω for all normalized generalized inverses of the complex matrix A.

TL;DR: In this article, nonnegative matrices which are equal to their Moore-Penrose generalized inverse are characterized, where the inverse is defined as the inverse of the original matrices.