An n-by-n matrix with n distinct eigenvalues is diagonalizable.

Created almost 9 years ago, updated about 8 hours ago

If an $n\times n$ matrix has $n$ distinct eigenvalues in $\mathbb F$, their eigenvectors are independent, so the matrix is diagonalizable over $\mathbb F$. This condition is sufficient but not necessary: the identity has a single eigenvalue and is already diagonal.

Like how this is organised?

Build your own knowledge tree on knowen.md: notes, decisions and tasks in one connected markdown graph, shared with your team and your AI agents.