Math Is Fun Forum

dervish

Member

Registered: 2008-05-22

Posts: 1

affine transformation invariance

hello,

I need to know if I have a triangle or another shape, upon applying an affine transform (X=ax+by+c,   Y=dx+ey+f)
which are the invariant measurements or the stable quantities between the shape before and the shape after,
if it's cross ratio, could you prove that ?

thanx in advance

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: affine transformation invariance

Try this mind experiment:
X = x and Y = dx + ey + f
This is simpler.

I have this hunch that if you take a matrix or grid or screen
of parallel and orthogonal lines, that is like the
regular setup for (x,y) plotting.
But now things are skewed.
Instead of squares in the grid, you will have diamonds
and parallelograms.
Both x and y axies will be turned and stretched, but
you can still plot points with such a setup of axis.

---

igloo myrtilles fourmis