Matrix inequalities by means of embedding

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Tian-Gang Lei
Ching-Wah Woo
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. 

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