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Notes on completely positive matrices

✍ Scribed by Shuhuang Xiang; Shuwen Xiang

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
326 KB
Volume
271
Category
Article
ISSN
0024-3795

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✦ Synopsis

Let A be a n Γ— n symmetric matrix and in the closure of inverse M-matrices.

Then A can be factored as A = BB r for some nonnegative lower triangular n Γ— n matrix B, and cp-rank A ~< n. If A is a positive semidefinite (0, 1) matrix, then A is completely positive and cp-rank A = rank A; if A is a nonnegative symmetric H-matrix, then A is completely positive and cp-rank A < n(n + 1)//2 -N -(n -/z), where /z is the number of connected components of the graph G(A).

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