當我們解一個遞迴關係的特徵方程式時，不管解得的根是相異根或者是重根，皆視這些跟產生的解之線性獨立為理所當然，因此很容易寫出此遞迴關係的通解乃是這些解的線性組合。在本文中，我們將透過廣義的范德蒙行列式(Generalized Vandermonde Determinant)的計算，很清楚地看出這些解之間的線性獨立。

　　When we solve a characteristic equation of a recurrence relation, no matter what the roots are distinct or not, we take the linear independence of these solutions producing by each root for granted. Basing on this fact, we can easily write out the general solutions of this recurrence relation by using linear combination of these solutions. In this paper, we will see the linear independence of these solutions very clearly through the calculation of Generalized Vandermonde Determinant.