Showing papers in "Linear Algebra and its Applications in 1975"

TL;DR: A linear map from M n to M m is completely positive iff it admits an expression Φ(A)=Σ i V ∗ i AV i where Vi are n×m matrices as mentioned in this paper.

TL;DR: For a matrix A which is diagonally dominant both by rows and by columns, bounds are given which can be used to give a lower bound for the smallest singular value.

TL;DR: There is a positive semidefinite biquadratic form that cannot be expressed as the sum of squares of bilinear forms as discussed by the authors, but it is expressed as a positive semi-definite quadratic form.

TL;DR: The Perron-Frobenius theory for square, irreducible, nonnegative matrices is generalized by studying the structure of the algebraic eigenspace of an arbitrary square nonnegative matrix corresponding to its spectral radius.

TL;DR: The error analysis for computing the QR decomposition by Givens transformations was given originally by Wilkinson for n × n square matrices, and later by Gentleman for N × p (p ⩽ n ) tall thin matrices as mentioned in this paper.

TL;DR: The main result of as mentioned in this paper is that A j D converges to A D if and only if there exists a j 0 such that core-rank A j =core-rank D for j ⩾ j 0.

TL;DR: A linear operator A is called reflexive if the only operators that leave invariant the invariant subspaces of A are the operators in the weak closure of the algebra of polynomials in A.

TL;DR: In this article, the authors summarize and extend some of the applicable solution procedures through a systematic use of operators which convert the matrix equation to vector and dimension-reduced vector forms.

TL;DR: In this paper, it is shown that associated with a polynomial a(x)=∑aipi(x) there is a matrix A which possesses several of the properties of the usual companion form matrix C. An alternative and possibly preferable form A' is also suggested.

TL;DR: In this article, the authors proved theorems of Perron-Frobenius type for a strongly irreducible operator A in the case that F = R, the real field and K is a full algebraically closed cone.

TL;DR: In this paper, the authors consider the case where A is an n × n complex-valued matrix, all of whose principal minors are distinct from zero, and there exists a complex diagonal matrix D, such that the spectrum of AD is a given set σ = {λ 1,…,λ n } in C.

TL;DR: In this article, the importance of the notion of splitting up, and the conditions under which it may be used and how it enables us to generate new algorithms are discussed, as well as the conditions for new algorithms.

TL;DR: In this paper, it was proved that a matrix is almost normal if and only if its singular values are close to the absolute values of its eigenvalues, and the dominating eigenvalue is well conditioned.

TL;DR: In this article, the author gave new proofs for certain inequalities previously established by the author involving sums of singular values of matrices A, B, C = A + B, and also when A and B are complementary submatrices of C.

TL;DR: In this article, generalized inverses of Boolean matrices are defined and the general form of matrices having generalized in-verses is determined, and an algorithm to compute a generalized inverse of a matrix, when it exists, is given.

TL;DR: In this article, the authors give theorems on the dimension of solution sets of semi-infinite systems of linear inequalities, and some results of Clark and Williams are generalized.

TL;DR: Second order difference equations with periodic coefficients have been shown to have a theory associated with them that is completely analogous to that for second order differential equations as discussed by the authors, and it is shown that from certain spectral data one can draw conclusions regarding the coefficients in the difference equation.

TL;DR: In this article, it was shown that Γ(K) is indecomposable if and only if K is the image of the nonnegative orthant under an orthogonal transformation.

TL;DR: In this paper, the authors consider a variety of questions in the context of Boolean designs and show that such matroids exist for all values of d except 2, 3, and 5.

TL;DR: In this paper, the authors find necessary and sufficient conditions on a polynomial ǫ(x) ϵ F[x] in order that it defines a permutation of (i) Dn, the diagonalizable matrices in Fn×n, (ii) Rn, all of whose roots are in F, and (iii) the matric ring itself.

TL;DR: In this paper, the authors examined combinatorial properties of extremal plane stochastic matrices of dimension three and obtained a lower bound for the number of connected extremal matrices.

TL;DR: Two generalizations of the well-known power method for computing the dominant eigenvalue of a matrix are given, based on the e-algorithm, and allow one to compute simultaneously all the eigenvalues and the Eigenvectors of a Matrix.

TL;DR: The paper will give a precise definition of the class of algorithms that are considered to evaluate these p bilinear forms, and characterize an optimal algorithm of this class, and relate the minimum number of multiplications used to the tensorial rank of the p matrices Bi.

TL;DR: In this paper, the convergence of the hyperpower iterative method for generating generalized inverses is studied. And the necessary and sufficient condition for the convergence is given in relation to the expansion.

TL;DR: In this paper, a scalar valued function d of the m -square matrices is defined, which depends on a subgroup G of S m and an irreducible representation of G .

TL;DR: In this paper, the usual construction of (v, q + 1,1)−BIBD's from vector spaces over GF ( q ) is generalized to the class of near vector spaces.

TL;DR: In this article, the most general 1-2 inverse of a matrix over a regular ring was found for the triplet BA'C. This result was used to give necessary and sufficient conditions for the invariance of BA' C, where A' is either a 1-inverse or a 1−2 inverse.

TL;DR: In this article, the numerical radius of matrices with non-negative entries was studied and explicit ways to compute it were given. And they also characterized positive matrices of equal spectral and numerical radii, i.e., positive spectral matrices.

TL;DR: In this paper, the authors investigated the matrix equation A2 =dI+λJ, where A is a rational circulant, and a necessary and sufficient condition is given for the existence of matrices A satisfying the equation, when such matrices exist, the construction and enumeration of solutions are given explicitly.