ENGLISH

Completely positive matrices

By Abraham Berman , Naomi Shaked-Monderer

Book information

Publisher
World Scienfic
Year
2003
ISBN
9812383689, 9789812383686, 9789812795212
Language
english
Format
DJVU
Filesize
888 kB (909273 bytes)
Pages
216\216
Topic
Mathematics Algebra
Library
Kolxo3
DPI
300
Scanned
yes
Time added
2009-07-20 03:45:11

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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