A linear map T:V→V on an inner product space V is self-adjoint if T equals its adjoint T*, that is, ⟨Tv,w⟩ = ⟨v,Tw⟩ for all v, w ∈ V. If V is finite-dimensional, then the matrix for T, with respect to an orthonormal basis, is symmetric (or Hermitian over ℂ). See spectral theorem.