一类特殊五对角和七对角行列式的计算

Determinant of a Special Class of Five-diagonal and Seven-diagonal Matrices

采用递推法研究了对称和非对称五对角行列式的通项公式.对于对称情形,给出显式表达式;对于非对称情形,通项公式为六个指数函数的线性组合.还得到对称七对角行列式的通项公式.

Using recurrent expressions, we obtain the general formula for the determinant of a class of symmetric and asymmetric five-diagonal matrices. For symmetric ones, the determinant is expressed explicitly. The determinant of an asymmetric five-diagonal matrix is a linear combination of the power of the six roots to its characteristic polynomial. We also provide the general formulae for symmetric seven-diagonal matrices.