Section 29.3 Terminology and notation
- scalar-triangular form
an upper or lower triangular matrix that has the same value repeated down the main diagonal
The remaining terminology and notation are relative to a square matrix \(A\) and a specific eigenvalue \(\lambda\) for that matrix.
- generalized eigenvector
a nonzero vector that is in the null space of the matrix \((\lambda I - A)^k\) for some positive integer \(k\)
- generalized eigenspace
the collection of all generalized eigenvectors for \(A\) corresponding to \(\lambda\text{,}\) along with the zero vector; denoted \(G_{\lambda}(A)\)
- generalized eigensubspace of degree \(k\)
the nullspace of the matrix \((\lambda I - A)^k\text{;}\) denoted \(E^k_{\lambda}(A)\)