On a Parametrization of Positive Semidefinite Matrices with Zeros
نویسندگان
چکیده
منابع مشابه
On a Parametrization of Positive Semidefinite Matrices with Zeros
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. The images of the maps are convex cones, and the maps can only be surjecti...
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In this note, we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique. Our results are similar to some inequalities shown by Bhatia and Kittaneh in [Linear Algebra Appl. 308 (2000) 203-211] and [Linear Algebra Appl. 428 (2008) 2177-2191].
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A real symmetric matrix M is completely positive semidefinite if it admits a Gram representation by positive semidefinite matrices (of any size d). The smallest such d is called the completely positive semidefinite rank of M , and it is an open question whether there exists an upper bound on this number as a function of the matrix size. We show that if such an upper bound exists, it has to be a...
متن کاملsingular value inequalities for positive semidefinite matrices
in this note, we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique. our results are similar to some inequalities shown by bhatia and kittaneh in [linear algebra appl. 308 (2000) 203-211] and [linear algebra appl. 428 (2008) 2177-2191].
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We show how the zero structure of a basis of the null space of a positive semidefinite matrix can be exploited to very accurately compute its Cholesky factorization. We discuss consequences of this result for the solution of (constrained) linear systems and eigenvalue problems. The results are of particular interest if A and the null space basis are sparse.
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2010
ISSN: 0895-4798,1095-7162
DOI: 10.1137/100783170