Getting Clear

 There I was, slaving away trying to understand how image rotation works

when it struck me. I has it all wrong about the dog picture. The eigenvector is

the white arrow, the one that doesn't change for the oberver. The yellow and green 

ones do change with the image.

                                                                  

The formula put forward for matrix rotation is the following:

                                                                            

I asked merlin to explain it to me.

                                                                                 

                                                                                   

On item 1, wasn't really clear on the arctan() function. We are now in polar coordinates,

and it is not an inversion of tan(x) values. Below, from AlloProf:

                                                                       

Made a graph showing what is going on using the GRAPH app:

                                                                                       

Arctan is a function, but only between - pi/2 and pi/2!! Below, Meta's explanation:

                                                                                        

My other difficulty was in using the trigonometric identities. I have I worked

with these in theory, but never in a practical way and could never seem to remember

them. Off the France for a site that helps me, clarifying what I need to know and

what I can always work out...

Trigonométrie : fonctions cosinus et sinus décryptées - Major Prépa (major-prepa.com)

The Math is Fun example is simple enough, with a 30 degree rotation, but one ends up

with an eigenvector on the complex plane...