ELA, Volume 11, pp. 66-77, April 2004, abstract.

Matrix Inequalities by Means of Embedding

Tian-Gang Lei, Ching-Wah Woo and Fuzhen Zhang

In this expository study some basic matrix inequalities
obtained by embedding bilinear forms <Ax,x> and
<Ax,y> into 2x2 matrices are investigated. 
Many classical inequalities are reproved or refined
by the proposed unified approach. Some inequalities 
involving the matrix absolute value |A| are given. 
A new proof of Ky Fan's singular value majorization 
theorem is presented.