Talk:Pfaffian

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I do not think one should try hard to change \times to x both ways it looks ugly, but hopefully with Mathml the first one will look better...

Tosha 15:29, 23 May 2004 (UTC)

[edit] Johann Friedrich Pfaff

Is this the guy? Tosha

Do you know the story? Gauss's mother asked a mathematician 'who is the best mathematician in Germany?' and the answer was 'Pfaff'. 'What about my son?' - 'Oh, he's the best mathematician in Europe!'. Pfaff was Gauss's teacher, in a sense.

Charles Matthews 09:04, 9 Sep 2004 (UTC)

Nice story, but is Johann Friedrich Pfaff is one who responsible for Pfaffian?

This web page says so: http://members.aol.com/jeff570/p.html. He had a brother JW Pfaff, who was also a mathematician, which I hadn't realised. Charles Matthews 18:55, 9 Sep 2004 (UTC)

Thank you Tosha

[edit] The Pfaffian in coordinates

(moved from generalized Gauss-Bonnet theorem)

Suppose given a coordinate coframe dxi. The curvature 2-form admits an expression {\Omega_i}^j relative to this coframe. Define the alternating Kronecker tensor

\delta_{j_1j_2\dots j_k}^{i_1i_2\dots i_k}

to be the identity endomorphism of \bigwedge^kT^*M. Then

Pf(\Omega)=\delta_{j_1j_2\dots j_n}^{i_1i_2\dots i_n}{\Omega_{i_1}}^{j_1}\wedge{\Omega_{i_2}}^{j_2}\wedge\dots\wedge{\Omega_{i_n}}^{j_n}

where repeated indices are summed.

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