1. Completely Positive Matrices
- Author
-
Abraham Berman, Naomi Shaked-monderer, Abraham Berman, and Naomi Shaked-monderer
- Subjects
- Matrices
- Abstract
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.
- Published
- 2003