% twoDexa (no parameters) script
%
% Defines a list of 2 x 2 matrices suitable for
% graphically exploring basic transformations of
% the plane.
%
% Typical call sequence:
% p=drawfig  % using drawfig.m, create a polygon)
% twoDexa    % initializes matrices A1, A2, A3...)
% lt2d(A1,p) % using rr.m, redraw p and overlay A1*p)
% lt2d(A2,p) % using rr.m, redraw p and overlay A2*p)
% ...
% lt2d(A3*C4,p)  % later also compose the transformations
% lt2d(inv(C6)*B3*C6,p)  
%
% Typical task: Precisely describe the effect of the
% linear transformation. Systematically organize the
% observations with the goal of KNOWING the effects of 
% any of these matrices....
%
% Author: Matthias Kawski. July 2000.
%         http://math.la.asu.edu/~kawski
%
% Update: July 24, 00: Corrections in help-paragraph.
%
A1=eye(2)
A2=3*eye(2)
A3=1/2*eye(2)
A4=-eye(2)
A5=-2/3*eye(2)
A6=ones(2)
A7=zeros(2)
A8=[1 1;0 1]
%
B1=diag([1,3])
B2=diag([1/2,1])
B3=diag([2/3,2])
B4=diag([1,-3])
B5=diag([-2,1/3])
%
C1=eye(2)
C2=[0 -1; 1 0]
C3=-eye(2)
C4=1/sqrt(2)*[1 -1;1 1]
C5=1/sqrt(2)*[1 1;-1 1]
C6=1/2*[1 -sqrt(3);sqrt(3) 1]
C7=1/2*[sqrt(3) 1;-1 sqrt(3)]
C8=1/2*[-sqrt(3) -1;1 -sqrt(3)]
%
D1=diag([1 -1])
D2=diag([-1,1])
D3=[0 1; 1 0]
D4=1/sqrt(2)*[1 1;1 -1]
D5=1/sqrt(2)*[-1 1;1 1]
D6=1/2*[1 sqrt(3);sqrt(3) -1]
D7=1/2*[-sqrt(3) 1;1 sqrt(3)]
D8=1/2*[-sqrt(3) -1;-1 sqrt(3)]