The Determinant And Inverse Matrix Of Three Special Toeplitz Matrices

In this thesis,we mainly analyze the determinants and inverse matrices of the following types of matrices with special structures:Hermitian Toeplitz matrix with complex Fibonacci numbers,skew-Hermitian Toeplitz matrix with Gaussian Fibonacci numbers,symmetric Toeplitz matrix with Fibonacci numbers,and their corresponding Hankel matrices.This thesis is divided into the following five chapters:The first chapter consists of three sections.The first section mainly introduces the ap-plication background of the Toeplitz matrix,and the domestic and foreign research situations of various structural matrices with famous numbers;in the second section,the definitions of these three special Toeplitz matrices and their corresponding Hankel matrices are given,but also gives the some useful lemmas;the third section mainly describes the main work of this paper.In the second chapter,the determinant and inverse matrix of Hermitian Toeplitz matrix and Hankel matrix with complex Fibonacci numbers are studied.In the first section,we construct the appropriate transformation matrices,and use them to get the determinant and inverse matrix of Hermitian Toeplitz matrix with complex Fibonacci numbers;in the second section,we use the relationship between the Toeplitz matrix and the Hankel matrix to obtain the determinant and inverse matrix of Hankel matrix with complex Fibonacci numbers;the third section gives examples of Hermitian Toeplitz matrix and Hankel matrix with complex Fibonacci numbers to verify the results.The third chapter and the fourth chapter study the determinant and inverse matrix of skew-Hermitian Toeplitz matrix with Gaussian Fibonacci numbers,symmetric Toeplitz matrix with Fibonacci numbers,and their corresponding Hankel matrices,respectively.First,we give the appropriate transformation matrices and use them to transform the structure matrix to obtain the determinant and inverse matrix of the structure matrix;then we use the relationship between the Toeplitz matrix and the Hankel matrix to obtain the determinant and inverse matrix of the corresponding Hankel matrix;finally,a concrete example is given to test the validity of the formulas.In the last chapter,we summarize the main work of the thesis,and give some suggestions and expectations to the research in future.