On The Properties Of The H-circulant Matrix

In the field of matrix theory research,the study of special circulant matrices has always been a hot direction.A large number of scholars at home and abroad continue to promote and extend classic circulant matrices.Based on previous researches on circulant matrices and H-circulant matrices,this paper discusses the correlation properties of H-circulant matrices with Tribonacci sequence,generalized Lucas sequence,and Chebyshev polynomials of the first and second types.The main contents of this paper are as follows:1.The determinant of the H-circulant matrix.The determinant based on the product of eigenvalues,and the method of factorization inverse transformation are used to discuss the H-circulant matrix and H-left circulant matrix whose elements are the first and second types of Chebyshev polynomials.A new matrix factorization method based on factorization is proposed,and the determinant of the H-circulant matrix whose elements are the Tribonacci sequence,the generalized Lucas sequence,the first and second types of Chebyshev polynomials is studied.2.The inverse of H-circulant matrix are studied by using the special structure and properties of H-circulant matrix.3.Spectral norm estimation of H-circulant matrices.The E norm of H-circulant matrices whose elements are two types of Chebyshev polynomials are discussed.The upper and lower bound estimates of the spectral norm of H-circulant matrices are calculated using some algebraic methods.