Minimal polynomial of a matrix

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