Abstract

Let A be an n×n positive definite symmetric real matrix with n eigenvalues λ1,λ2,…,λn and let x and y be two n×1 vectors with the angle ψ. 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.

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