Section 46.1 Terminology and notation
Each of the definitions below are for a linear operator \funcdef{T}{V}{V} on a finite-dimensional vector space V\text{.}- determinant
the determinant of the matrix \matrixOf{T}{B} for any choice of domain space basis \basisfont{B}
- trace
the trace of the matrix \matrixOf{T}{B} for any choice of domain space basis \basisfont{B}
- eigenvector
a nonzero vector \uvec{x} in the domain space such that the image vector T(\uvec{x}) is a scalar multiple of \uvec{x}
- eigenvalue
a scalar for which there exists an eigenvector \uvec{x} of operator T with T(\uvec{x}) = \lambda \uvec{x}
- eigenspace
the subspace of the domain space consisting of all eigenvectors of T that correspond to a specific eigenvalue \lambda\text{,} along with the zero vector
- E_\lambda(T)
notation for the eigenspace of operator T corresponding to the eigenvalue \lambda
- characteristic polynomial
the degree-n polynomial in the variable \lambda obtained by computing \det(\lambda I - T)
- c_T(\lambda)
notation for the characteristic polynomial of operator T
- characteristic equation
the polynomial equation \det(\lambda I - T) = 0