Regular element of a Lie algebra

In mathematics, a regular element of a Lie algebra or Lie group is an element whose centralizer has dimension as small as possible. In the specific case of nxn matrices over an algebraically closed field (such as the complex numbers), an element M is regular if and only if its Jordan normal form contains a single Jordan block for each eigenvalue. In that case, the centralizer is the set of polynomials of degree less than n evaluated at the matrix M, and therefore the centralizer has dimension n (but it is not necessarily an algebraic torus).