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.


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