Completely Positive Matrices

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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 c ompletely 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.Format: HardcoverNo of Pages: 216Imprint: World ScientificPublication date: 20030415 Show more