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

Authors: SÜLEYMAN SOLAK, MUSTAFA BAHŞİ

Abstract: Matrix commutator and anticommutator play an important role in mathematics, mathematical physic, and quantum physic. The commutator and anticommutator of two $n\times n$ complex matrices $A$ and $B$ are defined by $\left[ A,B% \right] =AB-BA$ and $\left( A,B\right) =AB+BA$, 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.

Keywords: Matrix commutator, Frobenius norm, Cauchy-Toeplitz matrix, exchange matrix

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