Now we are drilling down to the real issue (thanks, Alexei, with whom I had almost the same discussion off board earlier):
The fact is (and here I follow in some form Ian's line of argument) that geometric vectors in R2 and R3 have properties beyond the axiomatic definition of a vector space. Alas, that is what we are dealing with (at least the students of crystallography in BMC) here, and the warning not to treat complex numbers the same as what students know as 'vectors' seems appropriate. But I concede that this should be made more clear in the second edition of the offending side bar (where regurgitations of Wikipedia usually don't cut it). In this instance more accuracy at the expense of some parsimony can be justified. Cheers, BR -----Original Message----- From: Tim Gruene [mailto:[email protected]] Sent: Wednesday, April 02, 2014 2:13 PM To: [email protected] Cc: Bernhard Rupp; [email protected] Subject: Re: [ccp4bb] Structure factor equation -----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Dear Bernhard, I don't need to because the vector product is not a requirement for a vector space. It is something very specific to R^3, i.e. in most vector spaces you would have trouble defining a vector product - do you know the angle between two polynomials? Cheers, Tim On 04/02/2014 01:58 PM, Bernhard Rupp wrote: >> complex numbers together with the operation '+' defined in the >> canonical > way fulfill the axioms of a vector space, hence complex number are > vectors. > > Axiomatically yes but could you please define the vector products for > complex numbers? > > Thx, BR > - -- - -- Dr Tim Gruene Institut fuer anorganische Chemie Tammannstr. 4 D-37077 Goettingen GPG Key ID = A46BEE1A -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.12 (GNU/Linux) Comment: Using GnuPG with Icedove - http://www.enigmail.net/ iD8DBQFTO/7OUxlJ7aRr7hoRAnB3AJ0b9aI3TAVwama892RwLr8hQJAvQgCfRrDo fdADewbtB9zyOpgGXuZkULM= =t9ZA -----END PGP SIGNATURE-----
