Why are eigenvectors of an invertible matrix linearly independent?
2026-04-08 22:39:32.1775687972
Why are eigenvectors of an invertible matrix linearly independent?
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Who said they had to be? What about
$$\left[\begin{array}{cc}1 & 1\\0 & 1\end{array}\right]?$$
EDIT: Michael, below, is correct. In your PDF, the author is not asserting that an invertible matrix has linearly independent eigenvalues. Rather, the argument is that since the eigenvectors of $A$ are the columns of $P$, and $P$ is invertible, it must follow that the eigenvectors of $A$ are linearly indepedent (which is just using the fact that an invertible matrix has linearly independent columns).