Determinants And Norm Of A Circulant Matrix With The Product Of Pell And Pell-Lucas Sequences As Elements

On the basis of previous studies on skew circulant matrix and H-circulant matrix,the relevant properties of skew circulant matrix and H-circulant matrix whose elements are the product of Pell sequence and Pell-Lucas sequence are discussed.The main research contents of this paper are as follows:First,the determinant of n-order skew circulant matrix A_n is studied by constructing the transformation matrix.Using Euclidean norm formula,row maximum norm formula,column maximum norm formula,find the three norms of A_n,and then the formula obtain the upper and lower bounds of the spreads of A_n,and at the same time obtain the upper and lower bounds of the spectral norm of A_n from the relationship between the Euclidean norm and the spectral norm.Secondly,using the relationship between the skew cyclic quantity and the left skew circulant quantity,these conclusions of A_n are extended to the left skew circulant matrix B_n,that is,the determinant of B_n,Euclidean norm,row maximum norm,column maximum norm,and the upper and lower bounds of the spreads of B_n and the upper and lower bounds of its spectral norm can be obtained.Finally,using the properties of Pell and Pell-Lucas sequence and the basic theory of matrix,the Euclidean norm and the upper and lower bounds of the spectral norm of H-circulant matrixC_n containing the product of Pell and Pell-Lucas are studied.The article finally,numerical examples are used to further illustrate the correctness of the above conclusions.