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On the Controllability of Matrix Pairs $(A,K)$ with K Positive Semidefinite

โœ Scribed by Carlson, David; Datta, B. N.; Schneider, Hans

Book ID
118213008
Publisher
Society for Industrial and Applied Mathematics
Year
1984
Weight
522 KB
Volume
5
Category
Article
ISSN
0196-5212

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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