I need to find a surjective homomorphism from O3 onto SO3. The only thing that I can think of is a map which sends A to A^2, but it's not an homomorphism. Any idea? Thanks. D.
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Homomorph O3 -> SO3 watch
- Thread Starter
- 17-01-2010 10:43
- 17-01-2010 13:23
This should work if I've understood the notation (and not forgot some of algebra).
defined by if and if .
It's surjective since every A in SO(3) is also in O(3) and has determinant 1, so it's just mapped to itself. Checking it's a homomorphism can be done by considering the cases for determinant of A and B.