Oblique Peoeplitz And Perturbation Of The Rows And Columns And Inverses Of The Three-band Quasi-Toeplitz Matrix

In this thesis,we mainly analyze the determinants and inverse matrices of the following types of matrices with special structures:the Peoeplitz matrix with Perrin numbers,the Peankel matrix with Perrin numbers.Secondly,the special case of three-strip Toeplitz-like matrix with three-column perturbations,the determinant and inverse of(four Angle and two Angle perturbations),and the eigenvalues and eigenvectors are studied.Next,the universality of the determinants and inverse matrices of the three-banded Toeplitz-like matrix with three-column perturbations is studied,and a specific example is given to verify the conclusion.It is described in the following five chapters:The first chapter includes three sections.The first section mainly introduces the applica-tion background of Toeplitz matrix and the research status of various structural matrices con-taining famous Numbers at home and abroad.In the second section,the recurrence formulas of Perrin number(Rn),Fibonacci number(Fn),and Lucas number(Ln)are given.Nex-t,the transition transition matrix skew-peoeplitz and skew-peankel matrix,Lucas number Loeplitz matrix,and three-strip Toeplitz-like matrix Toeplitz matrix are described.Finally,five important lenumas are given.The third section describes the main work of this paper.In the second chapter,the determinant and inverse matrix of the skew-Peoeplitz matrix and skew-Peankel matrix with Perrin number are studied.In section one,the determinant and inverse matrix of the skew-Peoeplitz matrix and skew-Peankel matrix with Perrin number are obtained by constructing transformation matrix.In the second section,the relationship between the skew-Peoeplitz matrix and the skew-peankel matrix with Perrin number is given,resulting in the determinant and inverse matrix of the skew-peankel matrix with Perrin number.In the third chapter,the three-band disturbance of Toeplitz-like matrix determinant and inverse matrix was studied.Irn the first section,displacement matrix structure,the displacement matrix disturbance on the original matrix of role to the four corners,and region,and has four Angle disturbance of three strip Toeplitz matrix determinant and inverse matrix,at the same time has four Angle disturbance of three-strip of Toeplitz-like matrix similarity transformation,with four Angle disturbance of three strip Toeplitz-like matrix eigenvalue and eigenvector.In the second section,by constructing the permutation matrix,the matrix is applied to the original matrix with two angular perturbations,and the determinant and inverse matrix of the three-band Toeplitz-like matrix with two angular perturbations are obtained.In the last chapter,we summarize the main work of the thesis,and give some suggestions and expectations to the research in future.In the fourth chapter,the three-band disturbance of Toeplitz-like matrix determinant and general situation of inverse matrix is studied.In the first quarter and the second section by using the method of structural displacement matrix,and the method of using formula Sherman-Morrison-Woodbury,The determinants and inverse matrices of three-band Toeplitz-like matrices with three column perturbations are given respectively.In the third section,concrete examples are given to verify our results.The fifth chapter summarizes the main work of this paper and prospects the future work.