An application of the Vandermonde determinant
Junqin Xu, Likuan Zhao · International Journal of Mathematical Education in Science and Technology · 2006
Eigenvalue is an important concept in Linear Algebra. It is well known that the eigenvectors corresponding to different eigenvalues of a square matrix are linear independent. In most of the existing textbooks, this result is proven using mathematical induction. In this note, a new proof using Vandermonde determinant is given. It is shown that this method is much simpler.