Showing papers in "Linear Algebra and its Applications in 1973"

TL;DR: The Hadamard product of two matrices multiplied together elementwise is a rather neglected concept in matrix theory, and has found only brief and scattered application in statistical analysis.

TL;DR: In this paper, the authors introduced and analyzed certain classes of mappings on R n which represent nonlinear generalizations of the P - and S -matrices of Fiedler and Ptak, and of several closely related types of matrices.

TL;DR: In this paper, an algorithm for the calculation of eigenvalues and eigenvectors of centrosymmetric and related matrices is given, and some desirable properties of the algorithm are proved.

TL;DR: In this article, a numerically stable form of the Simplex method is presented with storage requirements and computational efficiency comparable with those of the standard form, which enables it to be readily generalized to quadratic and nonlinear programming.

TL;DR: Bounds for the displacement in the solution set of a system of perturbed linear inequalities are developed and results are applied to find estimates for changes in the Solution Set of a perturbedlinear program.

TL;DR: In this paper, it was shown that an n × n real triangular matrix A is a ΔSTP matrix if all its nontrivial minors are strictly positive, where A = LU where L is a lower triangular matrix and U is an upper triangular matrix.

TL;DR: In this paper, Taussky-Todd et al. generalized the canonical pair form theorem for nonsingular pairs of r.s. matrices and showed that the maximal number of blocks k and the block sizes dim Ai are determined by the factorization over C of ƒ (λ, μ) = det(λS + μT) for λ, μ e R.

TL;DR: In this paper, the theory of cyclic and diagonal products of elements of matrices was unified, and new results on diagonal similarity, diagonal equivalence, complete reducibility and total support were obtained.

TL;DR: In this article, the authors extend these results to the case where 9f is an arbitrary character and obtain an interesting decomposition of the tensor space, where the proof of a key lemma is simplified by using algebraic derivations.

TL;DR: In this article, the classical Perron-Frobenius theory has been extended to matrices which leave invariant a cone in the finite dimensional real space V. Although there is an extensive theory dealing with the lattice of faces of a polyhedral convex set, especially as parts of it extend to cones which are not polyhedral.

TL;DR: In this article, it was shown that the cardinal spline interpolation problem has a unique solution that grows like a power of |x| provided that all data grows like the Lagrange formula.

TL;DR: In this paper, the Drazin pseudoinverse of A is given by X = P s −k−1 A k B k+1 s−1, if A is nonsingular, k = 0, s = n, and this formula reduces to the well known result A −1 = P −1 n B n−1.

TL;DR: In this paper, it was shown that semidefinite quadratic forms in two by n variables are sums of squares of bilinear forms, where n is the number of variables.

TL;DR: In this article, an explicit expression for f (A) in terms of A 1, A 2, B, and its generalization to the case where a chain of invariant subspaces is known is given.

TL;DR: In this paper, the authors give a direct method for the construction of an operator norm with respect to which μ[A] can be made arbitrarily close to max Re(λi).

TL;DR: In this paper, the authors investigated the B-splines for the case of Hermite interpolation (γ > 1) and derived an explicit solution for the problem (1), where v = 0, 1, n, n.

TL;DR: The existence and uniqueness of a bounded solution for the linear equation in infinite matrix A x = b where A is strictly diagonally dominant and b is bounded was shown in this paper.

TL;DR: In this paper, it was shown that the logarithmic derivative of a square matrix A can be made equal to p for some operator norm in C n if and only if those eigenvalues of A with maximum real part are simple roots of the minimal polynomials for A.

TL;DR: In this article, ein Kriterium fur den Nachweis der Totalnichtnegativitat von Matrizen - insbesondere von Bandmatrizen- is proposed, das bisher bekannte Kriterien wesentlich vereinfacht.

TL;DR: In this article, the classical adjoint is applied to A -1 A ∗ and A 2, where A is a matrix for which H ( A ) is positive definite.

TL;DR: In this paper, it was shown that a convolution of two minimal G-functions is seldom minimal, and new results concerning the patterns of dependence of G -functions were established.

TL;DR: In this article, the solvability of linear equations with solutions in the interior of a closed convex cone is characterized, and Lyapunov's theorem characterizing stable matrices and a generalization of Stiemke's theorem of the alternative for complex linear inequalities.

TL;DR: In this paper, the boundary value problem for a linear first order system of ordinary differential equations with singularities at the endpoints of a finite interval is formulated, and the convergence of a projection method involving generalized splines is investigated.

TL;DR: Using expansions of generalized matrix functions by means of cyclic products and principal majors, conditions for regularity of equimodular classes of matrices were found in this paper, where the expansion of generalized matrices was used to find conditions for the regularity.

TL;DR: In this paper, the location of spectra and a partial description of a set cor-responding to a set of sets is given, and the proof is long and intricate and extends the work of N. Dimitriev and E. Dynkin who gave the characterization for n < 5.

TL;DR: In this paper, the eigenvalues of many retrocirculants were determined and a necessary and sufficient condition for a permutation matrix to commute with a retrocircular matrix was presented.