Real matrices have real minimal polynomials
= Real matrices have real minimal polynomials
{title2=$\overline{m_A}=m_A\quad(A\in M_n(\mathbb R))$}
The <minimal polynomial> of a real <matrix>, initially computed over the <complex numbers>, has real coefficients. Its coefficientwise <complex conjugate> is also a <monic polynomial> of the same degree annihilating the <matrix>. Uniqueness of the <minimal polynomial> forces the two <polynomials> to agree.