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

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.