Minimal polynomial of a matrix

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minimum polynomial of a matrix

Let $A$ be a matrix. The minimal polynomial of $A$ is the monic polynomial $g(\lambda)$ of lowest degree such that $g(A)=0$. It divides the characteristic polynomial of $A$ and, more generally, it divides every polynomial $f$ such that $f(A)=0$.


[a1] L. Mirsky, "An introduction to linear algebra" , Dover, reprint (1990) pp. 203ff
[a2] Ch.G. Cullen, "Matrices and linear transformations" , Dover, reprint (1990) pp. 178ff
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Minimal polynomial of a 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