-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Hi Bernhard,
I may not know what students know as vectors. I was told at school that the elements of a vector space are called vectors, and this was actually repeated at university. Later I realised that when you consider e.g. coordinate triplets as vectors there are quite a couple of useful tools from the "vector world", including the specialised vector product to e.g. calculate the distance between a point and a plane, but also that there are caveats, e.g. that when I want to rotate a molecule about its centre of mass I first must move that to the origin before applying the rotation matrix to its coordinates and then move them back. Could you provide an example where treating a complex number as a vector would lead a student to a mistake, or a misconception? Best, Tim On 04/02/2014 03:26 PM, Bernhard Rupp wrote: > 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:t...@shelx.uni-ac.gwdg.de] Sent: Wednesday, April 02, 2014 > 2:13 PM To: b...@hofkristallamt.org Cc: Bernhard Rupp; > CCP4BB@JISCMAIL.AC.UK Subject: Re: [ccp4bb] Structure factor > equation > > 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/ iD8DBQFTPBTGUxlJ7aRr7hoRAn4NAJ9UHApwlUk5aFGEB5QdcDT85Uu6aACgvvXV Jt+qdiCygYdkWHz1KGyBCDM= =ZCDF -----END PGP SIGNATURE-----
