defective matrix

Noun

 * 1)  A square (n×n) matrix that has fewer than n linearly independent eigenvectors, and is therefore not diagonalisable.
 * 2) * 1994, Sigal Ar, Jin-Yi Cai, Chapter 5: Reliable Benchmarks Using Numerical Stability, Proceedings of the Fifth Annual ACM-SIAM Symposium on Discrete Algorithms,, , page 41,
 * An n x n matrix A is a defective matrix if it has a defective eigenvalue.
 * Obviously, a Jordan block of dimension greater than 1, and a matrix whose Jordan canonical form has a Jordan block of dimension greater than 1, are defective matrices.

Usage notes
Equivalently, a matrix is defective if one of its eigenvalues has geometric multiplicity less than its algebraic multiplicity.