bo198214 Wrote:Well, I have it in my "Hütte Mathematische Tafeln":Gottfried Wrote:If their sign oscillate ...No, their sign doesnt oscillate.

The reason is simply: Some of the Eigenvalues are greater than 1 and hence the logarithm sequence does no more converge.

This seems to can be fixed with the series

which then properly converges.

To apply one of this series to a matrix, all eigenvalues must match the same bound separately.

I think, this settles this question for the most interesting cases.

For matrices with eigenvalues both <1 and >1 , which occurs with the Bs-matrixes for s outside the range 1/e^e ... e^(1/e) we need still workarounds, like the techniques for divergent summation. But this is then a completely different chapter. I'm happy, we have now arrived at a level of convergence of understanding of (one of?) the core points of concepts.

Gottfried

Gottfried Helms, Kassel