## Erratum on Jordan normal form

Several people pointed out to me an elementary misprint in
an earlier post . It’s corrected now, but it originally claimed that the Jordan normal form was determined by the characteristic
polynomial and the minimal polynomial up to $6 \times 6$ matrices. Actually, this is not true even for $4 \times 4$ matrices. (Consider, matrices $A$ with $ch_A(x)=(x-1)^4,\ \ m_A(x)=(x-1)^2$.) What I meant to say is that the JNF is determined by those two polynomials *and* the dimension of the eigenspaces (=number of Jordan blocks) for each eigenvalue. These three numbers might be referred to as the *elementary invariants* of a matrix.