**Definition 2.1.1.**

If *λ*0 is an eigenvalue of an *n* × *n* matrix *A*, then the dimension of the eigenspace corresponding to *λ*<sup>0</sup> is called the **geometric multiplicity** of *λ*0, and the number of times that *λ* − *λ*0 appears as a factor in the characteristic polynomial of *A* is called the **algebraic multiplicity** of *A.*

Eigenvalue and eigenvector have some specific features, which are easy to prove.

The following are some of the obvious features of eigenvalues of matrix A and corresponding eigenvector:
