Definition of minimal polynomial of a matrix

Created almost 9 years ago, updated about 8 hours ago

The minimal polynomial $m_A$ is the unique monic polynomial of smallest degree satisfying $m_A(A)=0$. It divides every annihilating polynomial, hence divides the characteristic polynomial. A matrix is diagonalizable over $\mathbb F$ iff $m_A$ splits there into distinct linear factors. For a scalar matrix $cI$, $m_A(t)=t-c$.

Like how this is organised?

Build your own knowledge tree on knowen.md: notes, decisions and tasks in one connected markdown graph, shared with your team and your AI agents.