An n-by-n matrix is diagonalizable if and only if the sum of the dimensions of the eigenspaces equals n.

Created almost 9 years ago, updated about 8 hours ago

A matrix is diagonalizable over $\mathbb F$ iff the sum of dimensions of its distinct eigenspaces over $\mathbb F$ is $n$. Eigenspaces for distinct eigenvalues form a direct sum. Their bases combine into an eigenvector basis exactly when the dimensions sum to $n$.

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