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Positive extension problems for a class of structured matrices

โœ Scribed by Vladimir Bolotnikov; Paul A. Smith


Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
316 KB
Volume
381
Category
Article
ISSN
0024-3795

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๐Ÿ“œ SIMILAR VOLUMES


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A matrix [ ai j( a)xi j ] is shown to be positive semidefinite or positive definite if the matrix [xi j] is positive semidefinite or positive definite and aij( a) belongs to a large class of functions of a. This class includes the reciprocals of the ath mean values of xii and xii in the cases where

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A function f from the symmetric group S n into R is called a class function if it is constant on each conjugacy class. Let d f be the generalized matrix function associated with f, mapping the n-by-n Hermitian matrices to R. For example, if f (ฯƒ ) = sgn(ฯƒ ), then d f (A) = det A. Let K n (K n (R)) d