Showing papers in "Linear Algebra and its Applications in 1977"

TL;DR: In this paper, the authors define rank (X) as the minimum number of triads whose sum is X, and dim1(X) to be the dimensionality of the space of matrices generated by the 1-slabs of X.

TL;DR: A survey of characterizations of nonsingular M -matrices from economics and mathematics literatures can be found in this article, where characterizations are grouped together in terms of their relations to the properties of (1) positivity of principal minors, (2) inverse-positivity and splittings, (3) stability and semipositivity and diagonal dominance.

TL;DR: In this article, a discrete inner product for which the associated sequence of monic orthogonal polynomials coincides with the sequence of appropriately normalized characteristic polynomorphisms of the left principal submatrices of the Jacobi matrix is constructed.

TL;DR: In this article, the classical inverse additive and multiplicative inverse eigenvalue problems for matrices are studied using general results on the solvability of polynomial systems and it is shown that in the complex case these problems are always solvable by a finite number of solutions.

TL;DR: This paper applies matrix splitting techniques and a conjugate gradient algorithm to the problem of minimizing a convex quadratic form subject to upper and lower bounds on the variables and presents the results of numerical experiments showing the effectiveness of the algorithm.

TL;DR: In this paper, the inverse M -matrix problem is formulated as follows: given a positive n × n matrix A =(a i j ) which has been scaled to have unit diagonal elements and off-diagonal elements which satisfy 0 y ⩽ a i j = a j = x A exists and is an M-matrix, then define an interpolation parameter s via x 2 = sy +(1− s ) y 2 ; then B is an m-additive matrix if s −1 ⩾ n −2.

TL;DR: In this paper, it was shown that if the least eigenvalue of A (G ) exceeds -1 − √ 2 and every vertex of G has large valence, then G is a generalized line graph.

TL;DR: A necessary and sufficient condition for all principal minors of a square matrix to be positive is given in this article, and a special subclass of such matrices called quasidominant matrices is also examined.

TL;DR: In this paper, sufficient conditions are given for every solution to be nonsingular when solutions exist when A, B and C are given square matrices and C is of rank one.

TL;DR: In this article, a theorem which characterizes irreducible and fully indecomposable matrices in an algebraic manner was proved, based on the Frobenius-Konig theorem.

TL;DR: A description of the lattice of hyperinvariant subspaces of a linear transformation on a finite-dimensional vector space is given, as well as implications between linear-algebraic and lattice-theoretic properties.

TL;DR: In this article, the index set of the nonzero decomposable symmetrized tensors, corresponding to Sm and λ, which are induced from a basis of the underlying vector space, is characterized.

TL;DR: In this paper, a spectral resolution for the inverse of a lambda-matrix L(λ) = ∑ i=0 l A i λ i where the A i are n × n complex matrices and det A l ≠ 0.

TL;DR: In this article, necessary and sufficient conditions for the existence of Hermitian solutions to the equations AH+HA ∗ =HA+A ∗ H=I were established for an n × n matrix with complex entries.

TL;DR: The centrosymmetric n × n permutation matrices are the extreme points of a convex subset of n 2 -dimensional Euclidean space, which are characterized by a very simple set of linear inequalities, thereby providing an interesting solvable case of a difficult problem posed by L. Mirsky as discussed by the authors.

TL;DR: In this paper, an accelerated version of simultaneous iteration for partial solution of the symmetric eigenproblem Px = λx is presented, where convergence together with sharp error bounds is obtained.

TL;DR: In this article, the authors prove a result which has as corollaries theorems of Hurwitz, Accola, Grothendieck, and Serre on automorphisms of Riemann surfaces.

TL;DR: A generalized rank of a matrix with entries in a commutative ring R with identity is discussed in this paper, where necessary and sufficient conditions for the solvability of the linear equation A x = b are derived, where x, b are vectors and A is a matrix having entries in either a Noetherian full quotient ring or a zero dimensional ring.

TL;DR: The method is based on Gaussian elimination and establishes explicit expressions for the elements of the resulting upper triangular matrix and is retraced for the case of a confluent type of generalized Vandermonde matrix.

TL;DR: In this paper, it is shown that if a matrix A comes close to satisfying the definition of the Moore-Penrose generalized inverse of A, A, A, then A is small.

TL;DR: In this paper, it was shown that for special families of amplification matrices G (A, B) a sufficient condition for power boundedness can be obtained by replacing the matrices by appropriate scalars, and so the problem is reduced to a scalar one.

TL;DR: In this paper, it was shown that there exists a permutation matrix P such that PMPT = LU, where L is a lower triangular M-matrix and U is an upper triangular singular M -matrix.

TL;DR: In this article, a complete classification of real linear transformations between two complex vector spaces in terms of matrices is given, where the matrices are matrices and the transformations are linear transformations.

TL;DR: In this article, conditions that are at least sufficient for the second order conditions of Lagrange optimization to hold are established, and conditions for Lagrange optimality to hold in general.

TL;DR: In this paper, general solutions are formulated for difference equations of the form ∑ i=0 l A i u r + i = ƒ γ, r = 1, 2,….

TL;DR: The main inertia theorem gives necessary and sufficient conditions that an n×n complex matrix A have no eigenvalues on any arbitrary circle, line, and certain other curves in the complex plane as mentioned in this paper.

TL;DR: The radial property of compound matrices is equivalent to the case of equality in the classical inequalities of H. Weyl relating products of eigenvalues and singular values of a linear operator.

TL;DR: In this article, a characterization of the maximum cardinality common independent sets of two matroids via an unbounded convex polyhedron is proved, confirming a conjecture of D.R. Fulkerson.

TL;DR: In this paper, the Moore-Penrose inverse of a block circulant matrix whose blocks are arbitrary square matrices is given in terms of the blocks of the matrix, where the blocks themselves are circulants.

TL;DR: In this paper, the Smith normal form of a matrix is computed using the technique of localization from commutative algebra, which yields short new proofs for a variety of matrix equivalence results.