Residual bounds for unitarily invariant norms on clustered eigenvalues
نویسندگان
چکیده
منابع مشابه
Inequalities for unitarily invariant norms
This paper aims to discuss some inequalities for unitarily invariant norms. We obtain several inequalities for unitarily invariant norms.
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This paper aims to present some inequalities for unitarily invariant norms. In section 2, we give a refinement of the Cauchy-Schwarz inequality for matrices. In section 3, we obtain an improvement for the result of Bhatia and Kittaneh [Linear Algebra Appl. 308 (2000) 203-211]. In section 4, we establish an improved Heinz inequality for the Hilbert-Schmidt norm. Finally, we present an inequality...
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Let A,B be nonzero positive semidefinite matrices. We prove that ‖AB‖ ‖A‖ ‖B‖ ≤ ‖A + B‖ ‖A‖+ ‖B‖ , ‖A ◦B‖ ‖A‖ ‖B‖ ≤ ‖A + B‖ ‖A‖+ ‖B‖ for any unitarily invariant norm with ‖diag(1, 0, . . . , 0)‖ ≥ 1. Some related inequalities are derived. AMS classification: 15A60, 15A45
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Let complex matrices $A$ and $B$ have the same sizes. Using the singular value decomposition, we characterize the $g$-inverse $B^{(1)}$ of $B$ such that the distance between a given $g$-inverse of $A$ and the set of all $g$-inverses of the matrix $B$ reaches minimum under the unitarily invariant norm. With this result, we derive additive and multiplicative perturbation bounds of the nearest per...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1997
ISSN: 0024-3795
DOI: 10.1016/0024-3795(95)00677-x