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.
- ISBN10 9812795219
- ISBN13 9789812795212
- Publish Date December 2003 (first published 1 January 2003)
- Publish Status Active
- Publish Country SG
- Imprint World Scientific Publishing Co Pte Ltd
- Format eBook
- Pages 218
- Language English