Suppose that $\ltdefn{T}{V}{V}$ is a linear transformation. Then there is a basis $B$ for $V$ such that the matrix representation of $T$ relative to $B$, $\matrixrep{T}{B}{B}$, is an upper triangular matrix. Each diagonal entry is an eigenvalue of $T$, and if $\lambda$ is an eigenvalue of $T$, then $\lambda$ occurs $\algmult{T}{\lambda}$ times on the diagonal.