Showing papers in "Linear Algebra and its Applications in 1982"

TL;DR: In this paper, for two p-dimensional random vectors X and Y with dispersion matrices Σ11 and Σ22, respectively, it is shown that the covariance matrix Ψ 0 of X and y that minimizes the L 2 distance between them can be obtained.

TL;DR: The computed eigenvalues are shown to be the exact eigen values of a matrix M+E where $\Vert E \Vert$ depends on the square root of the machine precision.

TL;DR: In this paper, a comprehensive expository study of nonnegative matrices which happen to be inverses of M-matrices is presented, aimed at an audience conversant with basic ideas of matrix theory.

TL;DR: In this article, a new version of the Buckingham pi theorem is presented which reveals the underlying mathematical structure of that classical result, and it is formulated without reference to physical quantities, units, dimensions, and so on.

TL;DR: In this article, a simple and natural generalization to 3-connected matroids is presented, which is used to prove Seymour's generalization of a theorem of Kelmans.

TL;DR: The spectrum of a locally finite countable graph is defined in this article, and some theorems known from the theory of spectra of finite graphs are extended to infinite graphs.

TL;DR: In this article, a brief account of the numerical radius of a linear bounded operator on a Hilbert space and some of its better-known properties are discussed, as well as applications to stability theory of finite-difference approximations for hyperbolic initial-value problems.

TL;DR: In this article, it was shown that such a tactical decomposition with more than one class has either a singleton point class, or just two point classes, one of which is a hyperplane.

TL;DR: In this paper, the second largest eigenvalue of a tree T has been shown to be λ 2(T)⩽lsqb(n−3)2rsqb12.

TL;DR: Methods of successive approximation for solving linear systems or minimization problems are accelerated by aggregation-disaggregation processes, characterized by means of Galerkin approximations, and this in turn permits analysis of the method.

TL;DR: In this article, the applicability of generalized inverses to a wide variety of problems in applied probability where a Markov chain is present either directly or indirectly through some form of imbedding is examined.

TL;DR: In this article, the existence and uniqueness of an M -matrix which is a square root of a real matrix with nonpositive off-diagonal elements is discussed and necessary and sufficient conditions for such a matrix to be an M-matrix are derived.

TL;DR: In this paper, the Richardson-type iterative method of Cimmino for solving linear equations is generalized to linear inequalities, which includes the generalized CIMMINO scheme, and convergence proofs are provided.

TL;DR: In this paper, the authors prove new inequalities of the form cp( eAe) 2 cp(eAtR), where A and B are n X n complex matrices, 1 < n < 00, and cp is a real-valued continuous function of the eigenvalues of its matrix argument.

TL;DR: In this paper, the least (Euclidean-) norm solution of a consistent linear equation Ax = b is given a determinantal form, which reduces to Cramer's rule if A is nonsingular.

TL;DR: In this paper, a generalized version of the convergence theorem of Sinkhorn and Knopp (1967) is proved and applied to show convergence for new methods for scaling square, nonnegative matrices to doubly stochastic form.

TL;DR: A method for solving the eigenvalue problem Ax = λBx, where A and B are real symmetric but not necessarily positive definite matrices, and B is nonsingular, which produces a tridiagonal pseudosymmetric form which is invariant under the HR transformations.

TL;DR: In this article, it was shown that every nonsingular totally positive m-banded matrix is the product of m totally positive one-bandsed matrices and, therefore, the limit of strictly mbanded totally positive matrices with linearly independent rows and columns.

TL;DR: In this article, it was shown that if a nonsingular linear transformation T on the space of n-square real symmetric matrices preserves the commutativity, where n ⩾3, then T(A) = λQAQt + Q(A), for some scalar λ, orthogonal matrix Q and linear functional Q

TL;DR: In this paper, the authors defined the closure of N 0 -matrices by letting λ ⩽ t, where t is the spectral radius of the principal submatrices of a matrix of order n − 1.

TL;DR: It is shown that Gutierrez Novoa's n-ordered sets are cryptomorphically the same as the oriented matroids, thereby establishing the existence of an axiomatization for oriented matroid in which the “oriented” bases of the matroid are the objects of paramount importance.

TL;DR: In this article, the authors studied the perturbation of the eigenvalues of a matrix pair Z = (A, B) of the Grassman manifold G n, 2 n and its eigen values as points in G 1, 2, the projective complex plane.

TL;DR: In this paper, Bhatia and Mukherjea compared the distances between the spectra of two matrices and gave optimal bounds on the eigenvalue variation of matrices by a factor of about two.

TL;DR: In this article, the shorting of an operator was extended to rectangular matrices and square matrices not necessarily hermitian nonnegative definite, and some applications of the shorted matrix in mathematical statistics were discussed.

TL;DR: The structure of sign-solvable and strongly sign- Solvable systems is studied here by a refinement of the graph-theoretic approach first suggested by Maybee, and both sign- solvability and strong sign-Solvability are characterized in terms of an associated digraph.

TL;DR: In this article, an upper bound for the relative error ∥ B D − A D ∥/∥ AD ∥ 2 and a lower bound for ∥ b D ∩ 2 under certain circumstances were given.

TL;DR: In this article, the Cramer rule for obtaining the least norm solution of a consistent system of linear equations Ax = b is shown to also provide the least-squared error solution in the inconsistent case, i.e. the solution A + b where A + is the Moore-Penrose inverse of A.

TL;DR: In this paper, a technique for proving D 1 AD 2 theorems for multidimensional matrices is given. And a generalization of the D 1AD 2 theorem to multi-dimensional matrices has been proposed.

TL;DR: In this paper, a uniform upper bound for differences of corresponding eigenvalues of two definite pairs was developed and proved to be a projective metric in the set of n × n definite pairs.