Relative perturbation bounds for weighted polar decomposition
نویسندگان
چکیده
منابع مشابه
Relative and Absolute Perturbation Bounds for Weighted Polar Decomposition
Let Cm×n, Cm×n r , C m ≥ , C m > , and In denote the set of m × n complex matrices, subset of Cm×n consisting of matrices with rank r, set of the Hermitian nonnegative definite matrices of order m, subset of C ≥ consisting of positive-definite matrices and n × n unit matrix, respectively. Without specification, we always assume that m > n >max{r, s} and the given weight matrices M ∈ C > ,N ∈ C ...
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Let M n (F) denote the space of matrices over the eld F. Given A2 M n (F) deene jAj (A A) 1=2 and U(A) AjAj ?1 assuming A is nonsingular. Let 1 (A) 2 (A) n (A) 0 denote the ordered singular values of A. We obtain majorization results relating the singular values of U(A + A) ? U(A) and those of A and A. In particular we show that if A; A2 M n (R) and 1 ((A) < n (A) then for any unitarily invaria...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2010
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2009.10.009