Results 11 to 20 of about 2,871 (211)
Products of positive semidefinite matrices
Linear Algebra and its Applications, 1988 The author proves that a matrix T is the product of finitely many nonnegative matrices if and only if det(T)\(\geq 0\) and in this case, five such matrices are sufficient.
Wu, Pei Yuan
openaire +2 more sources
Monotonicity of Positive Semidefinite Hermitian Matrices [PDF]
Proceedings of the American Mathematical Society, 1972 Inequalities which compare elements of the convex cone of positive semidefinite hermitian matrices with products of roots of elements are proved. They yield inequalities for Schur functions (generalized matrix functions) which, when specialized to the determinant, give a result of R. Bellman and L. Mirsky.
Merris, R., Pierce, Stephen
openaire +3 more sources
On a product of positive semidefinite matrices
Linear Algebra and its Applications, 1999 The matrix \(A\) is said to be positive semidefinite (psd) if there exists a matrix \(P\) such that \(PP^*=A\). If \(A\) and its conjugate transpose \(A^*\) have the same range space, then \(A\) is called EP. Necessary and sufficient conditions are given for the product of two positive semidefinite (psd) matrices to be EP. As a consequence, it is shown
Meenakshi, A.R., Rajian, C.
openaire +2 more sources
On permanents of positive semidefinite matrices
Linear Algebra and its Applications, 1985 Let A and B be positive semidefinite real symmetric matrices. Using properties of tensor products, \textit{T. Ando} [Hokkaido Math. J. 10, Special Issue, 10, No.1, 18-36 (1981; Zbl 0484.15006)] proved that \(per(A+B)\geq per A+per B\). In this paper, it is shown that the Binet- Cauchy formula for the permanent of a product of matrices can also be used ...
Bapat, Ravindra, Ravindra Bapat
openaire +2 more sources
On cone of nonsymmetric positive semidefinite matrices
Linear Algebra and its Applications, 2010 A square real matrix is called a \(P_0\) (\(P\)) matrix if all its principal minors are nonnegative (positive). Let \(\mathcal P_0\) and \(\mathcal P\) denote the classes of \(P_0\) and \(P\) matrices, respectively. The authors study the cone of nonsymmetric positive semidefinite matrices (NS-psd cone).
Wang, Yingnan, Xiu, Naihua, Han, Jiye
openaire +2 more sources
Low-rank matrix approximations over canonical subspaces
Journal of Numerical Analysis and Approximation Theory, 2020 In this paper we derive closed form expressions for the nearest rank-\(k\) matrix on canonical subspaces. We start by studying three kinds of subspaces. Let \(X\) and \(Y\) be a pair of given matrices. The first subspace contains all the \(m\times
Achiya Dax
doaj +7 more sources
Sparse Sums of Positive Semidefinite Matrices [PDF]
ACM Transactions on Algorithms, 2015 Many fast graph algorithms begin by preprocessing the graph to improve its sparsity. A common form of this is spectral sparsification, which involves removing and reweighting the edges of the graph while approximately preserving its spectral properties. This task has a more general linear algebraic formulation in terms of approximating sums of rank-one
Marcel Kenji de Carli Silva +2 more
openaire +3 more sources
On a Parametrization of Positive Semidefinite Matrices with Zeros [PDF]
SIAM Journal on Matrix Analysis and Applications, 2010 We study a class of parametrizations of convex cones of positive semidefinite matrices with prescribed zeros. Each such cone corresponds to a graph whose non-edges determine the prescribed zeros. Each parametrization in this class is a polynomial map associated with a simplicial complex supported on cliques of the graph.
Mathias Drton, Josephine Yu
openaire +2 more sources
On Some Matrix Trace Inequalities
Journal of Inequalities and Applications, 2010 We first present an inequality for the Frobenius norm of the Hadamard product of two any square matrices and positive semidefinite matrices. Then, we obtain a trace inequality for products of two positive semidefinite block matrices by using 2×2 ...
Ramazan Türkmen +1 more
doaj +2 more sources
TRACE INEQUALITIES OF POSITIVE SEMIDEFINITE MATRICES [PDF]
, 2006 In this paper, the trace inequalities involving special products of the positive semidefinite matrices are investigated. The trace inequalities between the Kronecker product and Kronecker sum of two matrices is obtained as in the short note Yang’s inequalities.
ÖZEL, Mustafa +3 more
openaire +3 more sources