Defective matrix

A matrix $A\in\mathbf C^{n\times n}$ is called non-defective if it has a set of $n$ independent eigenvectors (cf. Eigen vector). Otherwise it is called defective. The notion is of particular importance in numerical linear algebra.

References

 [a1] D.M. Young, R.T. Gregory, "A survey of numerical mathematics" , 2 , Dover, reprint (1988) pp. 741–743

Comment

A complex matrix $A$ is non-defective if and only if it is similar to a diagonal matrix: $\Delta = P A P^{-1}$.

References

• Lloyd N. Trefethen, David Bau III, Numerical Linear Algebra SIAM (1997) ISBN 0898713617
How to Cite This Entry:
Defective matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Defective_matrix&oldid=33752
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article