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.
متن کاملSome Inequalities for Unitarily Invariant Norms
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...
متن کاملSubmultiplicativity Vs Subadditivity for Unitarily Invariant Norms
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
متن کاملA Structure Theorem for the Polars of Unitarily Invariant Norms
The unitarily invariant norms of matrices, or operators, are essentially the symmetric norms of their singular values. A subclass of these norms depending upon only a few largest of the singular values is considered, and the polars of these norms are characterized. The result is then used to obtain generalizations of some well-known inequalities. The implications for operators on infinite-dimen...
متن کاملInequalities for Unitarily Invariant Norms and Bilinear Matrix Products
We give several criteria that are equivalent to the basic singular value majorization inequality (1.1) that is common to both the usual and Hadamard products. We then use these criteria to give a uniied proof of the basic majorization inequality for both products. Finally, we introduce natural generalizations of the usual and Hadamard products and show that although these generalizations do not...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2005
ISSN: 0024-3795
DOI: 10.1016/j.laa.2004.05.017