D: |a> |b> |c> |u> |v> |y>
 D: [A] [B] [C] [P1] [P2] [X] [Y] [Z]
 D: (c1) (c2) (c3) (d1) (d2) (d3)
 |a>=[1;0;0]
 |b> = [0;1;0]
 M: c=[0;0;1]
 A=|a><a|
 B=|b><b|
 C=|c><c|
 A+B+C
 D: [S]
 $
% now in normal matlab
 global S
 tmp=rand(3)
 tmp=tmp+tmp'
[ S dummy ] = eig(tmp)
 % back to Dirac
 Dirac
  S' S
M: u=S(:,1)
M: v=S(:,2)
M: y=S(:,3)
 <y|y>
 <y|a>
 |u><u|+|v><v|+|y><y|
 X=|a><a|
 X=X+|b><b|
 X |u>
 X |u> - |u>
 X X  |u>
 X X X X X X |u>
 X X + eye(3) - X