Showing papers in "Linear Algebra and its Applications in 1979"

TL;DR: In this paper, stable algorithms for the computation of the Kronecker structure of an arbitrary pencil were developed, which can be viewed as a generalization of the wellknown eigenvalue problem of pencils of the type LambdaI-A.

TL;DR: In this article, the concavity and convexity theorems for tensor products of positive definite matrices were proved for affine positive functions on (0, ∞) matrices.

TL;DR: By introducting a way of characterizing matrices in terms of their “distance” from being Toeplitz, a natural extension of recursive algorithms for finding the inverses of ToEplitz or displacement-type matrices is obtained.

TL;DR: In this article, a survey of necessary and sufficient conditions for a pair of quadratic forms to admit a positive definite linear combination and various extensions thereof is presented, as well as some extensions thereof.

TL;DR: In this paper, the problem of finding a necessary and sufficient condition for a matrix A (λ) to be λ-imbeddable in B (λ), where B is equivalent to a regular λ matrix having A(λ) as a submatrix, was solved in terms of the invariant polynomials of A (δ) and B (ε).

TL;DR: In this paper, the behavior of invariant factors of (generally rectangular) R -matrices under adjunction of rows was studied, and the relationship between the similarity invariants of a square F -matrix and those of a principal submatrix was studied.

TL;DR: In this paper, it was shown that if P is a polytope all of whose vertices are integer valued, then it is the solution set of a TDI system Ax ⩽ b where b is integer valued.

TL;DR: In this paper, a number of characterizations are given which are both necessary and sufficient for the uniqueness of a solution to a linear programming problem, and the characterisation is extended to linear programming problems.

TL;DR: In this paper, the commutativity rule for Schur complements was proved and the absorption rule for shorted operators was shown to be equivalent to Anderson's and Crabtree and Haynsworth's quotient formula for short operators.

TL;DR: In this article, a block-orthogonal decomposition method was used in conjunction with a nested dissection scheme to solve the least square adjustment problem in large-scale matrix problems.

TL;DR: In this paper, the eigenvalue problem Ax = λBx is shown to have a complete system of eigenvectors and that its eigenvalues are real.

TL;DR: In this paper, a new proof based on the Perron-Frobenius theory of nonnegative matrices is given of a result of Hurwitz on the sharpness of the classical Enestrom-Kakeya theorem for estimating the moduli of the zeros of a polynomial with positive real coefficients.

TL;DR: In the QZ algorithm, the eigenvalues of Ax = Ax = λ$Bx are computed via a reduction to the form λ-Bx, where λ is upper triangular as mentioned in this paper.

TL;DR: In this article, a necessary and sufficient condition for solvability of the matrix equation AX − YB = C was established, which differs from that given by W.E. Roth.

TL;DR: In this paper, the authors characterize those matrices with nonzero diagonal elements whose inverses are tridiagonal and show that such matrices have an interesting structure, which is similar to the structure of Jacobi matrices.

TL;DR: In this article, it was shown that a n × n Jacobi matrix is uniquely determined by its n eigenvalues and by the selected set of n − 1 entries in the matrix.

TL;DR: In this article, a formula for inverting general band matrices is established, taking a simple form when the matrices are tridiagonal, and as a special case it includes the Bukhberger-Emel'yanenko algorithm for symmetric tridimensional matrices.

TL;DR: In this article, the lower half of the inverse of a lower Hessenberg matrix is shown to have a simple structure, and the result is applied to find an algorithm for finding the inverse for a tridiagonal matrix.

TL;DR: The least eigenvalue of the 0-1 adjacency matrix of a graph is denoted λ G as discussed by the authors, and all graphs with G ≥ −2 are characterized.

TL;DR: A positive definite symmetric matrix is called a Stieltjes matrix provided that all its off diagonal elements are non-positive as mentioned in this paper, and functions which preserve the class of non-stieltje matrices are characterized.

TL;DR: In this paper, it was shown that these criteria remain valid over arbitrary commutative rings, and they can be reduced to the case of Artinian rings, where a simple argument with

TL;DR: In this article, it was shown that r c is a generalized matrix norm if and only if C is nonscalar and tr C ≠ 0, where tr C = diag (1,0,…,0).

TL;DR: In this paper, the authors studied the congruence relation between nonsingular symmetric and skew-symmetric matrices in the set of all real matrices A,B and showed that A and B are S-congruent if there is a nonsingul upper triangular matrix R such that A = RTBR.

TL;DR: In this article, the authors give a necessary and sufficient condition for a 3 × 3 doubly stochastic matrix to be orthostochastic and then use this result to consider the structure of the sets W (A,B) = {Diag UAU∗ : U ∈ U3} and W(A and B) = [Tr UAU ∗ B: U ∆ U3], where ∗ denotes the transpose conjugate.

TL;DR: In this article, an accelerated generalization of Newton's method for finding matrix p th roots is developed in a form suitable for finding the positive definite p th root of a positive definite matrix.

TL;DR: It is shown that pivoting is unnecessary when solving an unsymmetric positive definite linear system Ax=b if the quantity ‖ST −1 S‖ 2 ‖A’ 2 is suitably small with respect to the working machine precision.

TL;DR: The number of nonscalar multiplications required to evaluate a general family of bilinear forms is investigated and an upper bound is obtained which is about half that obtained from naive arguments.

TL;DR: In this article, the inverse of a circulant matrix having only three nonzero elements in each row (located in cyclically adjacent columns) is derived analytically from the solution of a recurrence equation.

TL;DR: In this article, the authors explore various matrix-theoretic aspects of the class C ∩P for real square matrices having positive principal minors, which is a generalization of Z-matrices.

TL;DR: In this article, the problem of simultaneously putting a set of square matrices into the same block upper triangular form with a similarity transformation was considered, and a result linking the size of the largest block to polynomial identities was obtained.