An inequality for doubly stochastic matrices
Copyright policy )An inequality for doubly stochastic matrices
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· Frobenius eigenvalue of A. The relationship between these two inequalities is exhibited.
Positive matrices and their generalizations; cones of matrices, Miscellaneous inequalities involving matrices, Numerical computation of matrix norms, conditioning, scaling, Stochastic matrices
Positive matrices and their generalizations; cones of matrices, Miscellaneous inequalities involving matrices, Numerical computation of matrix norms, conditioning, scaling, Stochastic matrices
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