An inequality for complex matrices
نویسندگان
چکیده
منابع مشابه
Ela an Eigenvalue Inequality and Spectrum Localization for Complex Matrices∗
Using the notions of the numerical range, Schur complement and unitary equivalence, an eigenvalue inequality is obtained for a general complex matrix, giving rise to a region in the complex plane that contains its spectrum. This region is determined by a curve, generalizing and improving classical eigenvalue bounds obtained by the Hermitian and skew-Hermitian parts, as well as the numerical ran...
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Using the notions of the numerical range, Schur complement and unitary equivalence, an eigenvalue inequality is obtained for a general complex matrix, giving rise to a region in the complex plane that contains its spectrum. This region is determined by a curve, generalizing and improving classical eigenvalue bounds obtained by the Hermitian and skew-Hermitian parts, as well as the numerical ran...
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Let A be an n-square (0, 1)-matrix, let ri denote the i-th row sum of A, i = 1 ..... n, and let per(A) denote the permanent of A. Then per(A) ~< H ri q~/-2,.1 I + V T where equality can occur if and only if there exist permutation matrices P and Q such that PAQ is a direct sum of l-square and 2-square matrices all of whose entries are 1. I f A = (ai~) is an n-square mat r ix then the permanent ...
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Interrelated inequalities involving doubly stochastic matrices are presented. For example, if B is an n by n doubly stochasti c matrix, x any nonnega tive vector and y = Bx, the n XIX,· •• ,x" :0:::; YIY" •• y ... Also, if A is an n by n nonnegotive matrix and D and E are positive diagonal matrices such that B = DAE is doubly s tochasti c, the n det DE ;:::: p(A) ... , where p (A) is the Perron...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1974
ISSN: 0024-3795
DOI: 10.1016/0024-3795(74)90058-5