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
โฆ LIBER โฆ
Positive extension problems for a class of structured matrices
โ 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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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 (ฯ ) = sgn(ฯ ), then d f (A) = det A. Let K n (K n (R)) d