Distinct Eigenvalues Have Linearly Independent Eigenvectors

We prove that if a matrix has distinct eigenvalues, then it necessarily has linearly independent eigenvectors. As a corollary of this, we show that there are at most the dimension of underlying space number of eigenvalues. Furthermore, we show that if there are n (dimension of the matrix) number of distinct eigenvalues, then the matrix will be diagonalizable. #mikethemathematician, #mikedabkowski, #profdabkowski