Eigenvalue of a Linear Operator

Let $V$ be a \reftext{def:vector-space-2026a}{complex vector space}, let $T$ be a \reftext{def:linear-operator-2026a}{linear operator} on $V$, and let $\mu$ be a \reftext{def:complex-numbers-2026a}{complex number}.

The number $\mu$ is an \textbf{eigenvalue of $T$} if there exists a vector $x\in V$ that is an \reftext{def:eigenvector-eigenvalue-2026a}{eigenvector of $T$ with eigenvalue $\mu$}.