Sentence:  Theorem (7.5.2) then says that every positive semidefinite <WSD>matrix</WSD> is a convex combination of <WSD>matrices</WSD> that lie on extreme rays. 
Meaning of the word marked with <WSD> tags:  A rectangular arrangement of numbers or terms having various uses such as transforming coordinates in geometry, solving systems of linear equations in linear algebra and representing graphs in graph theory.