COMPLETELY POSITIVE MATRICES
| By: | Berman Abraham; Shaked-monderer Naomi |
| Publisher: | World Scientific Publishing |
| Print ISBN: | 9789812383686 |
| eText ISBN: | 9789812795212 |
| Edition: | 0 |
| Format: | Page Fidelity |
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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 invaluable book 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.