๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Majorizations of hadamard products of matrix powers

โœ Scribed by George Visick

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
376 KB
Volume
269
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

โœฆ Synopsis

This paper presents a number of intervening terms for the weak majorization ,IJ'i(A" '1 a Qh(A') for k=l,Z ,..., n, where A, B > 0. More specifically, it proves for r E (0, l] that a zfikhi(AB) for k = l,...,n.

It also shows that behind many of these inequalities are stronger ones.

๐Ÿ“œ SIMILAR VOLUMES

Fractional Hadamard powers of positive s
Fractional Hadamard powers of positive semidefinite matrices
โœ P. Fischer; J.D. Stegeman ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 197 KB

We consider the class S n of all real positive semidefinite n ร— n matrices, and the subclass S + n of all A โˆˆ S n with non-negative entries. For a positive, non-integer number ฮฑ and some A โˆˆ S + n , when will the fractional Hadamard power A โ™ฆฮฑ again belong to S + n ? It is known that, for a specific

On the range of a Hadamard power of a po
On the range of a Hadamard power of a positive semidefinite matrix
โœ Xiaosong Sun; Xiankun Du; Dayan Liu ๐Ÿ“‚ Article ๐Ÿ“… 2006 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 88 KB

For any n ร— n complex matrix A and any integer k 1, we prove that the span of image of the map x โ†’ (Ax) (k) is equal to the range of (AA \* ) (k) , where X \* and X (k) denote the conjugate transpose and the kth Hadamard power of a matrix X, respectively. This settles a conjecture, due to Gorni and

Warped products of Hadamard spaces
Warped products of Hadamard spaces
โœ Stephanie B. Alexander; Richard L. Bishop ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Springer ๐ŸŒ English โš– 169 KB