Group homomorphisms and isomorphisms
General · Mathematics
Study notes
Q: Show det: GL(2,ℝ) → ℝ* is a homomorphism. Find its kernel. det(AB) = det(A)det(B) ✓: HOMOMORPHISM! Kernel: det = 1: SL(2,ℝ) (special linear!)! First isomorphism: GL/SL ≅ ℝ* (image!)! (Surjective: any r: diag(r,1)!) Structure preserved: products → products!