| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4602614 | Linear Algebra and its Applications | 2008 | 6 Pages |
Abstract
Let A be an n×nn×n positive definite symmetric real matrix with n eigenvalues λ1,λ2,…,λnλ1,λ2,…,λn and let x and y be two n×1n×1 vectors with the angle ψψ. This paper proves the following inequality|xTAy|2⩽maxi,jλicos2ψ2-λjsin2ψ2λicos2ψ2+λjsin2ψ22(xTAx)(yTAy).It is a unified version of the Cauchy–Schwarz inequality and the Wielandt one.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Zi-zong Yan,