Completely Positive Matrices

Completely positive matrices (not to be confused with the completely positive maps in operator theory) arise from the related concept of completely positive quadratic forms in the theory of block designs. In this graduate or advanced undergraduate text, Berman (Israel Institute of Technology) and Shaked-Monderer (Emek Yezteel College) describe the conditions necessary and sufficient for complete positivity and the bounds for the cp-rank. They present the material in modules within three chapters, with topics ranging from preliminary studies on theory, complex positivity and analysis of the cp-rank. They include exercise and a list of notations. Annotation c2004 Book News, Inc., Portland, OR (booknews.com)