ENGLISH

Completely positive matrices

By Abraham Berman , Naomi Shaked-Monderer

Book information

Publisher
World Scienfic
Year
2003
ISBN
9789812383686, 9812383689
Language
english
Format
DJVU
Filesize
675 kB (691500 bytes)
Pages
218\218
Topic
Mathematics Algebra
Scanned
yes
Time added
2009-08-06 05:14:26

Description

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.

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