Showing papers in "Linear Algebra and its Applications in 1972"

TL;DR: In this paper, the authors studied the relationship between the number of solutions to the complementarity problem, w = Mz + q, w⩾0, z ⩾ 0, w T z=0, the right-hand constant vector q and the matrix M. The main results proved in this work are summarized below.

TL;DR: In this paper, it is shown that testing the quasi-convexity of a quadratic function on the nonnegative (semipositive) orthant can be reduced to an examination of finitely many conditions.

TL;DR: In this article, the relationship between geometric properties of a graph and the spectrum of its adjacency matrix was studied and lower bounds for α, β, γ were given in terms of the spectrum.

TL;DR: In this paper, the relationship between matrix pencils and matrix games is studied and a canonical form is derived from which it is easy to state conditions for existence of such solutions, and it is shown that ordinary elimination methods and eigenvalue routines may be used to find pencil solutions.

TL;DR: In this article, it was shown that the irreducible M K matrices are a subset of the matrices in the class M (K, K 2 ) defined by Fiedler and Ptak.

TL;DR: In this article, a new constructive proof of a theorem of Hardy, Littlewood, and Polya relating vector majorization and doubly stochastic matrices is presented, and conditions on the vectors which guarantee that the corresponding matrices will be direct sums are given.

TL;DR: In this article, the generalized inverses of n × n matrices over the Boolean algebra of order two are applied to the study of directed graphs and nonnegative matrices.

TL;DR: In this article, it was shown that the Schur function for the symmetric group of degree n and χ is defined by d χ H (Y) = ∑ σϵH χ(σ) ∏ i=1 n y iσ(i) for any n -square matrix Y = ( y ij ).

TL;DR: In this article, a characterization of real matrices A which satisfy E n −1 ( PA ) = E n−1 ( A ) for all n × n permutation matrices P.