Results 21 to 30 of about 5,271,349 (211)
On the cone of positive semidefinite matrices [PDF]
Linear Algebra and its Applications, 1987 An as yet unsolved problem in matrix theory is to classify those linear transformations of the \(n\times n\) complex matrices which leave the cone, PSD, of positive semidefinite Hermitian matrices invariant. The present note surveys the known results on the structure of the cone PSD, and some of the results concerning linear transformations which map ...
Hill, Richard D., Waters, Steven R.
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On a product of positive semidefinite matrices [PDF]
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.
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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
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On permanents of positive semidefinite matrices [PDF]
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
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On cone of nonsymmetric positive semidefinite matrices [PDF]
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
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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
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Gap inequalities for non-convex mixed-integer quadratic programs [PDF]
, 2011 Laurent and Poljak introduced a very general class of valid linear inequalities, called gap inequalities, for the max-cut problem. We show that an analogous class of inequalities can be defined for general non-convex mixed-integer quadratic programs ...
Galli, Laura +8 more
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Binary positive semidefinite matrices and associated integer polytopes [PDF]
, 2012 We consider the positive semidefinite (psd) matrices with binary entries, along with the corresponding integer polytopes.We begin by establishing some basic properties of these matrices and polytopes.
Sorensen, M M, Letchford, A N
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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
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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
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