On the Frobenius norm of commutator of Cauchy-Toeplitz matrix and exchange matrix

Abstract

: Matrix commutator and anticommutator play an important role in mathematics, mathematical physic, and quantum physic. The commutator and anticommutator of two n × n complex matrices A and B are defined by [ A, B ] = AB − BA and ( A, B ) = AB + BA , respectively. Cauchy-Toeplitz matrix and exchange matrix are two of the special matrices and they have excellent properties. In this study, we mainly focus on Frobenius norm of the commutator of Cauchy-Toeplitz matrix and exchange matrix. Moreover, we give upper and lower bounds for the Frobenius norm of the commutator of Cauchy-Toeplitz matrix and exchange matrix.