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.
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