Showing papers in "Linear Algebra and its Applications in 1985"

TL;DR: The Euclidean distance matrix D of order n is symmetric with elements − 1 2 d ij 2, where dii=0 as discussed by the authors, and the dimensionality of D is defined as the least value of p=rank(X) of any generating X; in general p+1 and p+2 are also acceptable but may include imaginary coordinates.

TL;DR: In this article, a characteristic equation for the spectrum of an eigenvalue problem on c 2 -networks is deduced, and those special cases in which the spectrum depends mainly on the structure of the abstract graph belonging to the c 2 network are investigated.

TL;DR: In this article, the maximum spectral radius for (0, 1)-matrices with k2 and k2+1 1's, respectively, and for symmetric (1, 1) matrices with zero trace and e=k21's (graphs with e edges) was determined.

TL;DR: In this article, a short, self-contained treatment using linear algebra and matrix theory is provided for establishing maximal periods, underlying structure, and choice of starting values for shift-register and lagged-Fibonacci random number generators.

TL;DR: In this article, the authors provide an exposition of alternative approaches for obtaining maximum likelihood estimators (MLE) for the parameters of a multivariate normal distribution under different assumptions about the parameters.

TL;DR: In this paper, an extension of Szego's theorem for the singular values of Tn[f] was given for the case where f(Θ) is not real valued.

TL;DR: For cubic shape tensors, the typical rank of a given shape (n, m, l) was shown to be ⌈ n3/(3n − 2) ⌉ (n ≠ 3).

TL;DR: The LM N-inverse as mentioned in this paper is a generalized inverse of a linear transformation A: →, where and are arbitrary finite dimensional vector spaces, defined using only geometrical concepts of linear transformations.

TL;DR: Upper bounds for the maximum modulus of the subdominant roots of square nonnegative matrices are obtained using a unified approach that yields or improves upon most of the bounds that have been obtained so far.

TL;DR: In this article, a vector x is said to majorize a vector y if y lies in the convex hull of the orbit of x under a group G and every convex G -invariant function of y is less than the same function of x .

TL;DR: In this paper, a formula for the characteristic polynomial of an n th order Toeplitz band matrix, with bandwidth k n, in terms of the zeros of a k th degree polynomials with coefficients independent of n is given.

TL;DR: In this paper, an iterative generalization of Cimmino's scheme for solving linear inequalities is considered. But it is not suitable for implementation on computers with parallel processors, and convergence from any starting point for both consistent and nonconsistent systems is not guaranteed.

TL;DR: For undirected graphs without loops or multiple edges, the star degree of a bipartite graph can also be characterized by the multiplicity of the root 1 of per( xI − B ), where B = D + A as discussed by the authors.

TL;DR: In this paper, it was shown that the spectrum of a positive semidefinite matrices is majorized by the Schur product of the matrices of A and B. The results are applicable to spectra of Schur products of positive semi-ideal matrices.

TL;DR: In this paper, it was shown that the inequality (1/χ( id ))d χ (A) ⪕ per A holds for a variety of characters χ including the irreducible ones corresponding to the partitions ( n − 1, 1,1) and (n − 2,1, 1) of n.

TL;DR: In this article, a simple counting rule for local identifiability of the factor analysis model is given generically, and a counterexample shows that these conditions are not necessary in general.

TL;DR: A characterization of the spread of a normal matrix is used to derive several simple lower bounds for the spread and comparisons are made with several known bounds.

TL;DR: In this article, a 2-cyclic block SOR method was proposed to solve the least square problem in geodesy, where A1 is easily formed and is large and sparse.

TL;DR: For any real nonnegative definite matrices M 1 and M 2, necessary and sufficient conditions for M 1 ⩾ M 2 are presented in this paper for the comparison of linear models.

TL;DR: The lower bound is achieved in all even dimensions for (and only for) adjacency matrices of complete bipartite graphs with equal parts.

TL;DR: In this article, the authors present a three-phase inversion procedure for generalized inverses, which is a special case of generalized inverse GAG = G. The geometry of {2}-inverses can be derived starting from generalized GAGs.

TL;DR: The question of whether a real matrix is symmetrizable via multiplication by a diagonal matrix with positive diagonal entries was reduced to the corresponding question for M -matrices and related to Hadamard products in this paper.

TL;DR: In this paper, the authors established a bound for the spectral variation of two complex n × n matrices A, B in terms of ∥ A ∥, ∥ B ∥.

TL;DR: The duality result of Olkin and Pukelsheim (1982) is extended to a wide class of problems of minimizing a real-valued function of certain elements of a symmetric matrix subject to this matrix being nonnegative definite.

TL;DR: The functional equation f(xy ) = f( x ) g ( y )+ g ( x ) f( y ) + h( x) h( y) as discussed by the authors is solved where f, g, h are complex functions defined on a group.

TL;DR: In this article, the principal results of the algebra of Kronecker products in a way which relates them directly to the abstract algebra of tensor products are discussed. But only one of these definitions is viable and it is argued that the other definitions are not consistent with the classical representation of linear algebra via matrix theory.

TL;DR: In this article, the identity map, the transpose map, and the map τ(x)− 1 n (x) Tr (x)-1 n in the matrix algebra Mn are illustrated, providing parametric examples of maps which are not k+1-positive but which satisfy the matrix Schwartz inequality of order k for 1 ⩽ k⩽ n − 1.

TL;DR: In this paper, sufficient conditions for the existence of a positive solution (componentwise) of a linear nonhomogeneous system of equations with positive coefficients are given. But these conditions are not applicable to the case of linear non-homogeneous systems.

TL;DR: In this paper, the maximum spectral radius for 0-1 matrices with m 2 + l ones for l = 2 m, 2 m − 3 for all m and for a fixed l and m > M ( l ).

TL;DR: In this article, the authors characterized Lyapunov diagonally stable real H-matrices with respect to principal submatrix rank property. And they applied their results to the numerical abscissas of real matrices.