Mon 2/29/00
* homework
* more matrix multiplication:
* permutations as "1's in multiplication table" matrices
- determinants + or - for even, odd permutations
* 3x3 rotations about x,y,z : 3 parameter orthogonal group O(3)
* 6 parameter lorentz group; boosts in special relativity
* NEW STUFF:
Direct product of 2 groups:
* ordered pairs (g,h) (g',h') = (g g', h h')
* examples: C2 X C3
assign:
(1) (If you know determinants). Show that the determinant of a matrix
with an odd number of columns swapped in the identify matrix is -1.
(2) If X and Y are boosts in the X and Y directions, find the matrix
for X Y X' Y' and show that it's a rotation. (Lorentz Group)
(3) 10.11 in Armstrong: Show that D_2n is isomorpnic to D_n X Z_2
when n is odd. (What happens when n is even?)