###### Example 4.2.4

The diagonal matrix \(\left[\begin{array}{rr} 3 \amp 0 \\ 0 \amp 3 \\ \end{array}\right]\) has the characteristic equation \((3-\lambda)^2 = 0\text{.}\) There is a single eigenvalue \(\lambda = 3\) having multiplicity \(m = 2\text{,}\) and we saw earlier that \(\dim E_3 = 2 \leq m = 2\text{.}\)