01/18/2008, 10:28 PM

Hi -

maybe this was already discussed here, but rereading Aldrovandi/Freitas I find a remark, which seems to contradict my diagonalization in the exp(x)-1-iteration.

They state pg 16, concerning the triangular Bell-matrix, (U or S2 in my notation)

Did I overlook something?

Gottfried

R. Aldrovandi and L.P.Freitas; Continuous iteration of dynamical maps; 1997; Online at arXiv physics/9712026 16.dec 1997

wikipedia:diagonalizable

wikipedia:normal matrix

maybe this was already discussed here, but rereading Aldrovandi/Freitas I find a remark, which seems to contradict my diagonalization in the exp(x)-1-iteration.

They state pg 16, concerning the triangular Bell-matrix, (U or S2 in my notation)

Quote:"(...) Bell matrices are not normal, that is, they do not commute with their transposes. Normality is the condition for diagonalizability. This means that Bell matrices cannot be put into diagonal form by a similarity transformation. (...)"In my understanding this remark is a bit misleading; the normality-criterion applies only, if an orthonormal similarity transform is requested, which is usually also called a rotation. But here we are able to do a similarity transform using triangular matrices, which even allows exact powerseries-terms for arbitrary size of matrices.

Did I overlook something?

Gottfried

R. Aldrovandi and L.P.Freitas; Continuous iteration of dynamical maps; 1997; Online at arXiv physics/9712026 16.dec 1997

wikipedia:diagonalizable

wikipedia:normal matrix