Defective matrix

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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.


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


  • D.M. Young, R.T. Gregory, "A survey of numerical mathematics" , 2 , Dover, reprint (1988) pp. 741–743
  • Lloyd N. Trefethen, David Bau III, Numerical Linear Algebra SIAM (1997) ISBN 0898713617
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Defective matrix. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article