An Expression of Arbitrary Positive Integer Powers for One Type of Tridiagonal Matrices

摘要

In the [7] and [8] papers, J.Rimas researched the tridiagonal matrix with elements 1,0,0,...,0,1 in principal and 1,1,1,...,1,1 in neighboring diagonals, and gave its high power of expression. In this new paper, we will derive the general expression of the high power of tridiagonal matrix with elements 1,0,0,...,0,0 in principal and 1,1,1,...,1,1 in neighboring diagonals. This new paper will use the polynomial of the recurrence relation and trigonometric nature, discuss the tridiagonal matrix, calculate high-order matrix into the low-order matrix of the matrix and launch its high power of expression.