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

✍ Scribed by Carlson, David

Book ID
118213087
Publisher
Society for Industrial and Applied Mathematics
Year
1994
Tongue
English
Weight
458 KB
Volume
15
Category
Article
ISSN
0895-4798

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For any n Γ— n complex matrix A and any integer k 1, we prove that the span of image of the map x β†’ (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