Showing papers in "Linear Algebra and its Applications in 1970"

TL;DR: In this paper, characterizations of copositive plus matrices are given, together with relationships of these matrices with positive semidefinite matrices and their quadratic forms.

TL;DR: In this paper, it was shown that if the first k columns of a polynomial matrix are expressed as linear combinations of the remaining δ(a) − k columns (which are linearly independent), then the greatest common divisor is given by the coefficients of column k + 1 in these expressions.

TL;DR: The explicit solution of (IP) when A has full row rank is used here to derive an iterative method for solving the general (IP), which is shown to be a dual method with multiple substitution.

TL;DR: In this paper, it was shown that if the number of vertices is large enough, the existence of a graph with the same spectrum as the line graph of a complete bipartite graph and which is not isomorphic to it is equivalent to a symmetric Hadamard matrix with constant diagonal.

TL;DR: Theorem 9.1 as mentioned in this paper shows that T preserves rank k matrices if T(Rk) ⊆ Rk, where Rk is the set of all rank j matrices in Mm,n(F).

TL;DR: Two alternative algorithms for solving Gomory's asymptotic integer programming algorithm, which consists of the simplex method, transformation of a matrix into Smith's normal form, and a group minimization algorithm.

TL;DR: A convex quadratic program has Kuhn-Tucker conditions which are necessary and sufficient, and suggest a dual problem as mentioned in this paper, and these conditions may be formulated in a convenient schematic notation which leads to a finite class of equivalent problems displaying Cottle's duality.

TL;DR: In this article, it was shown that when the primal feasible set is nonempty and bounded, the dual set is bounded if and only if all variables, including slacks, are unbounded.

TL;DR: In this article, the authors considered symmetric n × n matrices over a field F finite dimensional extension of the rationals and proved the Hilbert-Landau theorem for such matrices.

TL;DR: For a Hermitian n × n matrix of the form H = P ρQ ρ Q ∗ R of which all the eigenvalues of the s × s submatrix P are greater than all eigen values of the square t × t sub-matrix R, it is proved in this paper that the s greater eigen value of H is increasing and the remaining t eigenvalue of H are decreasing functions of the absolute value of the complex variable ρ.

TL;DR: In this article, the behavior of the eigenvalues of a finite birth and death matrix with subdiagonal elements was investigated, and the most negative eigenvalue was strictly decreasing along a straight line ai = rbj, r > 0.