A matrix and its transpose have the same eigenvalues/characteristic polynomial.

Created almost 9 years ago, updated about 8 hours ago

A square matrix and its transpose have the same characteristic polynomial because $\det(tI-A^T)=\det((tI-A)^T)=\det(tI-A)$. Therefore their eigenvalues, including algebraic multiplicities, agree. Their eigenvectors need not agree. Adjoint eigenvalues are complex conjugates instead.

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