An Appplication of Conjugation

Notes for Math 371 by M. Flashman

We denote

by L ... the translation of the plane by the vector <-1,-2> ,

by T'... the rotation of the plane by 90 degrees about the origin (0,0), and

by L

Then T =

So

L[ |
x |
]=[ |
x-1 |
]=[ |
x' |
] |

y |
y-2 |
y' |
||||

T'[ |
x' |
]=[ |
-y' |
] |
||

y' |
x' |
|||||

L^{-1}[ |
-y' |
]=[ |
-y' +1 |
]=[ |
-(y-2)+1 |
] |

x |
x' +2 |
x -1 +2 |
||||

and thus we have |
||||||

T[ |
x |
]=[ |
3-y |
] |
||

y |
x+1 |

Here is the visualization of T as a map in Winplot using: (x,y)==>(3-y,x+1)

Plane before the Application of T |
Plane after the Application of T |