Eigenvalue

linear-algebra

Definition

Eigenvalue

Let $T:V\to V$ be a linear operator on a vector space $V$ over a field $F$. A scalar $\lambda \in F$ is an eigenvalue of $T$ if there exists a non-zero vector $x\in V$ such that

$$Tx=\lambda x$$

Equivalently, $\lambda$ is an eigenvalue if $T$ has an associated eigenvector $x\ne 0$.