A matrix $A$ is called defective if $A$ has an eigenvalue $\lambda$ of multiplicity $m > 1$ for which the associated eigenspace has a basis of fewer than $m$ vectors; that is, the dimension of the eigenspace associated with $\lambda$ is less than $m$. Use the eigenvalues of the following matrices to determine which matrices are defective.
Example:
$A = \begin{bmatrix} 7 & 0 & 0 \\ 2 & 7 & 2 \\ -2 & 0 & 5 \end{bmatrix}$.
I found the eigenvalues= 7,7,5 where 7 has a multiplicity of 2.
My Problem is: How to decide a matrix is defective? Am I supposed to consider only the value 7 or both 7 and 5 because the definition says it is defective if eigenspace associated with the value is less than $m$.
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