On the Norms of RFMLR-Circulant Matrices with the Exponential and Trigonometric Functions

On the Norms of RFMLR-Circulant Matrices with the Exponential and Trigonometric Functions

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In this paper, based on combinatorial methods and the structure of RFMLR-circulant matrices, we study the spectral norms of RFMLR-circulant matrices involving exponential forms and trigonometric functions.Firstly, Kitchen Tools we give some properties of exponential forms and trigonometric functions.Furthermore, we study Frobenius norms, the lower and upper bounds for the spectral norms of RFMLR-circulant matrices involving exponential forms and trigonometric functions by some ingenious algebra methods, and then we obtain Horse Martingales new refined results.