Matrix Inequalities by Means of Embedding
Electronic Journal of Linear Algebra
Eigenvalue, Majorization, Matrix absolute value, Matrix inequality, Matrix norm, Normal matrix, Positive semidefinite matrix, Singular value, Spread, Wielandt inequality
In this expository study some basic matrix inequalities obtained by embedding bilinear forms 〈Ax, x〉 and 〈Ax, y〉 into 2 × 2 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.
Lei, Tian-Gang; Woo, Ching-Wah; and Zhang, Fuzhen, "Matrix Inequalities by Means of Embedding" (2004). Mathematics Faculty Articles. 73.