Improved Cauchy-Schwarz Inequality for Matrices

Huang Hong

Abstract: In this paper, using Hermite-Hadamard Integral Inequality we give an improvement of the matrix Cauchy-Schwarz inequality which was due to Bhatia and Davis in [5], and also obtain a further improvement of a refined matrix Cauchy-Schwarz inequality which was due to Ali et al. in [2].

Keywords: Unitarily invariant norms, Cauchy- Schwarz inequality, Hermite-Hadamard Integral Inequality, Positive semidefinite