A note on the Frobenius conditional number with positive definite matrices

摘要

In this article, we focus on the lower bounds of the Frobenius condition number. Using the generalized Schwarz inequality, we present some lower bounds for the Frobenius condition number of a positive definite matrix depending on its trace, determinant, and Frobenius norm. Also, we give some results on a kind of matrices with special structure, the positive definite matrices with centrosymmetric structure.