# Minimal polynomial of a matrix

From Encyclopedia of Mathematics

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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 $f(A)=0$.

#### References

[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 |

**How to Cite This Entry:**

Minimal polynomial of a matrix.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Minimal_polynomial_of_a_matrix&oldid=32058

This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article