Determinants And Spectral Norms Of Circulant Matrices Involving Fibonacci Polynomials And Generalized K-horadam Sequences

Circulant matrix,a long-term and fruitful research subject,has good structure and numerous properties.Among them,the research on the norm and determinant of circulant matrices are particularly active.This paper combines two special second order sequence with the H-circulant matrix,the row first-plus-rlast r-right(RFPr Lr R)circulant matrix and the first and the last difference r-circulant(FLDcirc_r)matrix,and studies the spectral norm and determinant of these circulant matrices.The main research content of this paper are as follows:1.The calculate method of Euclidean norm of H-circulant matrix involving Fibonacci polynomials is given based on the matrix form of the recurrence relation for Fibonacci polynomials.The upper and lower bound of spectral norm of H-circulant matrix involving Fibonacci polynomials is studied by using the matrix decomposition.2.Utilizing the special structure properties of circulant matrix and generalized k-Horadam numbers,and combining the inverse transformation of polynomial factoring,the determinants of the RFPr Lr R circulant matrix and FLDcirc_rmatrix with generalized k-Horadam numbers are studied,respectively.