Loading [MathJax]/extensions/TeX/boldsymbol.js
Skip to main content

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)