Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4600606 | Linear Algebra and its Applications | 2012 | 9 Pages |
Abstract
We shall prove the inequalities|||(A+B)(A+B)∗|||⩽|||AA∗+BB∗+2AB∗|||⩽|||(A-B)(A-B)∗+4AB∗|||for all n×nn×n complex matrices A,BA,B and all unitarily invariant norms ∣∣∣·∣∣∣.∣∣∣·∣∣∣. If further A,BA,B are positive definite it is proved that∏j=1kλj(A♯αB)⩽∏j=1kλj(A1-αBα),1⩽k⩽n,0⩽α⩽1,where ♯α♯α denotes the operator means considered by Kubo and Ando and λj(X),λj(X),1⩽j⩽n,1⩽j⩽n, denote the eigenvalues of XX arranged in the decreasing order whenever these all are real. A number of inequalities are obtained as applications.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Jagjit Singh Matharu, Jaspal Singh Aujla,