An n-by-n complex matrix has n eigenvalues counting multiplicity

Created almost 9 years ago, updated about 8 hours ago

Every complex $n\times n$ matrix has $n$ eigenvalues counting algebraic multiplicity, since its characteristic polynomial has degree $n$ and splits over $\mathbb C$. There need not be $n$ distinct eigenvalues or independent eigenvectors. A real matrix can lack real eigenvalues.

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