Completely Positive Matrices (Google eBook)

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World Scientific, Jan 1, 2003 - Mathematics - 206 pages
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A real matrix is positive semidefinite if it can be decomposed as A=BB'. In some applications the matrix B has to be elementwise nonnegative. If such a matrix exists, A is called completely positive. The smallest number of columns of a nonnegative matrix B such that A=BB' is known as the cp rank of A. This work focuses on necessary conditions and sufficient conditions for complete positivity, as well as bounds for the cp rank. The methods are combinatorial, geometric and algebraic. The required background on nonnegative matrices, cones, graphs and Schur complements is outlined.
  

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Contents

Complete positrvity
61
CP rank
139

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Page 6 - A is an eigenvalue of A, and x is an eigenvector.
Page viii - This research was supported by the fund for promotion of research at the Technion.
Page 3 - Here \A\ denotes the matrix whose elements are the absolute values of the corresponding elements in A.

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