7 Mar
2011
7 Mar
'11
6:30 p.m.
On Monday 07 March 2011 01:58:27 Fred Lunnon wrote:
An "affine transformation", it sez 'ere, is x -> A x + b where A, b are fixed matrix, vector and x is a (finite dimensional) vector variable. Ah: I knew there was something dodgy about this notion --- these transformations are not closed under composition! So that has to be patched up by immediately abandoning the Cartesian coordinates motivating it, and moving homogeneous coordinates instead.
A(Cx+d)+b = (AC)x + (Ad+b). In what sense are these transformations not closed under composition? -- g