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 $f(A)=0$.
|[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|
Minimal polynomial of a matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Minimal_polynomial_of_a_matrix&oldid=32058