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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.

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