Showing papers in "Linear Algebra and its Applications in 1969"

TL;DR: In this article, a theory and algorithms for asymptotic integer programs are described and a class of polyhedra is introduced, which are cross sections of more symmetric higher dimensional polyhedras whose properties are then studied.

TL;DR: In this article, it was shown that if A is a block-H matrix, the corresponding Jacobi and Gauss-Seidel block iterations converge, and a supplementary result on the corresponding overrelaxation is also given.

TL;DR: In this article, the authors proved that symmetric irreducible tridiagonal matrices and their permutations are the only symmetric matrices (of order n > 2) the rank of which cannot be diminished to less than n - 1 by any change of diagonal elements.

TL;DR: In this article, the authors define the following notation and conventions: M > 0 if M is a matrix and all mij > 0; if M >0 but M # 0, and they call M a positive matrix, and in this case M strictly positive.

TL;DR: In this paper, the authors considered the problem of upper bounds for |λ(A)| π(A), where A is a positive matrix, π is any one of its eigenvalues and π (A) is the biggest eigenvalue.

TL;DR: In this paper, necessary and sufficient conditions for the product of EPr matrices with entries from an arbitrary field are given, and results about the reverse order law for generalized inverses of products of these matrices are included.

TL;DR: Zusammenfassung as discussed by the authors showed that some of the ideas used in [2] in discussing the additive inverse problem can be applied to the multiplicative problem as well, i.e., the problem of finding a real diagonal matrix V such that V A possesses prescribed iegenvalues s1, s2, etc.

TL;DR: A special class of periodic continuants shows itself to be factorizable by means of the zeros of a Chebyshev polynomials of second kind.

TL;DR: In this article, a theorem which establishes a link between linear algebra and combinatorial mathematics is presented with an elementary constructive proof, where the maximum among the ranks of the matrices in P(N) is equal to the minimum among their term ranks, where P(n) is the family of matrices obtained from an arbitrarily given matrix N through pivotal transformations.

TL;DR: In this paper, relations connecting the maximum and minimum moduli and the real part of the eigenvalues of a matrix are given connecting the two moduli, and the relationship between them is shown by examples.

TL;DR: In this article, the authors consider an algebra A over the field C of complex numbers and show that if p is a norm on A then, under appropriate assumptions, (1) is again a norm.