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Weak matrix majorization

✍ Scribed by Francisco D. Martínez Pería; Pedro G. Massey; Luis E. Silvestre


Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
346 KB
Volume
403
Category
Article
ISSN
0024-3795

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📜 SIMILAR VOLUMES


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Let f be a convex function defined on an interval I , 0 α 1 and A, B n × n complex Hermitian matrices with spectrum in I. We prove that the eigenvalues of f (αA + (1α)B) are weakly majorized by the eigenvalues of αf (A) + (1α)f (B). Further if f is log convex we prove that the eigenvalues of f (αA +

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A matrix A is said to be matrix majorized by a matrix B, written A ≺ B, if there exists an n × n row stochastic matrix X such that A = BX. This is a generalization of multivariate majorization. In this paper, we characterize the linear operators that strongly preserve the matrix majorization.

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We desire to find a correlation matrix R of a given rank that is as close as possible to an input matrix R, subject to the constraint that specified elements in R must be zero. Our optimality criterion is the weighted Frobenius norm of the approximation error, and we use a constrained majorization a

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