Difference between revisions of "Defective matrix"
From Encyclopedia of Mathematics
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(Comment: Non-defective iff diagonalisable, cite Trefethen & Bau (1997)) |
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<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> D.M. Young, R.T. Gregory, "A survey of numerical mathematics" , '''2''' , Dover, reprint (1988) pp. 741–743</TD></TR></table> | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> D.M. Young, R.T. Gregory, "A survey of numerical mathematics" , '''2''' , Dover, reprint (1988) pp. 741–743</TD></TR></table> | ||
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| + | ====Comment==== | ||
| + | A complex matrix $A$ is non-defective if and only if it is [[Similar matrices|similar]] to a [[diagonal matrix]]: $\Delta = P A P^{-1}$. | ||
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| + | ====References==== | ||
| + | * Lloyd N. Trefethen, David Bau III, ''Numerical Linear Algebra'' SIAM (1997) ISBN 0898713617 | ||
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| + | [[Category:Special matrices]] | ||
| + | [[Category:Numerical analysis and scientific computing]] | ||
Revision as of 20:42, 17 October 2014
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
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