The calculation of the tridiagonal determinant

The elements on the main diagonal of a tridiagonal determinant and the elements on the first sub-diagonal above and below the main diagonal are not all zero, and the other elements are all zero, which is called a tridiagonal determinant. The characteristic of the tridiagonal determinant is that the whole structure remains unchanged after reducing one dimension. The calculation methods of tridiagonal determinant include elimination method, expansion recursion method and mathematical induction method.