Calculation of Determinant of a Special Toeplitz Matrix

Abstract

Toeplitz matrix is one of special forms of structural matrix, and its study plays an important role in the theory of matrix and computational mathematics. This paper mainly discusses the solution of the determinant of a special Toeplitz matrix, three recursive relations are obtained by using the properties of the determinant, and the solution of the determinant of the special Toeplitz matrix is transformed into the solution of the determinant of the tridiagonal Toeplitz matrix, the arithmetic difference and quasi-arithmetic sequence are constructed by combining the recursive relations to find the general term expression, and the exact solution of the determinant of the special Toeplitz matrix is given. As application, the positive qualitative determination problem of this special Toeplitz matrix is solved.