Page "Spectrum of a matrix" Paragraph 3

Let V be a finite-dimensional vector space over some field K and suppose T: V → V is a linear map.

An eigenvector of T is a non-zero vector x ∈ V such that Txλx for some λ ∈ K.

The value λ is called an eigenvalue of T and the set of all such eigenvalues is called the spectrum of T, denoted σ < sub > T </ sub >.