On The Determiant And Spectral Norms Of Circulant Matrix Involving The Generalized Fibonaci Polynomials And Chebyshev Polynomial

The kind of circulant matrix have special structure and properties.In ren-cent years,it’s an active topic that circulant matrices have been studied in many aspects.In particular,circulant matrices,r-circuant matrix,the RFPrLrR cir-culant matrix,the RLPrFrL circulant matrix,the RSFPLR circulant matrix and the RSLPFL circulant matrix which are different from common matrix are considered respectively.Many scholars have learned comprehensively circulant matrices basing on the special properties.Firstly,the fundamental definitions and theory of various special circulant matrices,famous polynomials have been given.Secondly,let the famous poly-nomials apply to circulant matrices.The main research findings of this paper are:1.I have discussed the determinants of some special circulant matrix,on one hand,the main purpose of this paper is using the inverse factorization of polynomial to give the determinants of the RSFPLR circulant matrices and RSLPFL circulant matrices involving the generalized Fibonacci polynomials,on the other hand,I have studied the determinants of RFPrLrR circulant matrix,the RLPrFrL circulant matrix involving Chebyshev polynomials.2.the spectral norms of γ-circuant matrix including generalized Fibonacci polynomials are given by using algebraic methods.