If the equation has a repeated root, can you tell without evaluating in the matrix if that repeated root corresponds to more than one eigenvector?
2026-03-27 04:38:48.1774586328
Can you tell how many eigenvectors a matrix has from just the characteristic equation?
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No. Consider $$ \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}, $$ and $$ \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}. $$ They have the same characteristic polynomial, but not the same eigenvectors.