A defective matrix is a square matrix over the complex numbers that has no vector basis of eigenvectors. Equivalently, some eigenvalue has geometric multiplicity smaller than its algebraic multiplicity.
Defective Matrix
See also
Diagonalizable Matrix, Eigenvector, Exceptional Point, Jordan Canonical FormExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Defective Matrix." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DefectiveMatrix.html