Algebraic Multiplicity

Definition

$Alg(\lambda )$ of an eigenvalue $\lambda$ is the number of times that it occurs as a root of the Characteristic Polynomial of $T$

Example

For the matrix

$$\left[\begin{array}{cccc}1& 1& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 2& 0\\ 0& 0& 0& 3\end{array}\right]$$

We get that the Characteristic Polynomial is: $(\lambda -1)(\lambda -2{)}^2(\lambda -3)$

• It follows that the eigenvalues are: ${\lambda }_1=1,{\lambda }_2=2,{\lambda }_3=3$ Then, $Alg(1)=2,Alg(2)=1,Alg(3)=1$