Spectrum of a Matrix

The spectrum of a matrix is the set of all Eigenvalues.

Definition

• Given $A\in {\mathbb{F}}^{n\times n}$.
• The set of Eigenvalues is called the spectrum of $A$ denoted by: $\sigma (A):=\{\lambda \in \mathbb{F}|A\alpha =\lambda \alpha \text{ for some non-zero vector }\alpha \}$