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On the range of a Hadamard power of a positive semidefinite matrix

โœ Scribed by Xiaosong Sun; Xiankun Du; Dayan Liu

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
88 KB
Volume
416
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

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 Tutaj-Gasiล„ska, related to the study of the Jacobian Conjecture.

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