We consider the class S n of all real positive semidefinite n ร n matrices, and the subclass S + n of all A โ S n with non-negative entries. For a positive, non-integer number ฮฑ and some A โ S + n , when will the fractional Hadamard power A โฆฮฑ again belong to S + n ? It is known that, for a specific
Hadamard powers and totally positive matrices
โ Scribed by Shaun M. Fallat; Charles R. Johnson
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 124 KB
- Volume
- 423
- Category
- Article
- ISSN
- 0024-3795
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๐ SIMILAR VOLUMES
A square real matrix A is said to have signed d-power, if the sign pattern of the power A d is uniquely determined by the sign pattern of A. A is said to have totally signed powers if A has signed d-powers for all positive integers d. A is said to be d-powerful if all the non-zero terms in the expan
We say that a rectangular matrix over a (in general, noncommutative) ring with identity having a positive part is generalized totally positive (GTP) if in all nested sequences of socalled relevant submatrices, the Schur complements are positive. Here, a relevant submatrix is such either having k con