- #1
spin_100
- 15
- 1
In Michael Tinkham's book, Group theory and Quantum Physics, he derives a theorem that any matrix representation can be converted to an equivalent transformation which is unitary. i.e ##A## is converted to ## B = S^-1 A S ## such that B is unitary. My question is how is it possible to find such a transformation? We know similarity transformations preserve the determinant, so if we start with a matrix A with ## det(A) \neq 1 ## then it is not possible to get a matrix B with a determinant equal to 1 since we know the determinant of a Unitary matrix is 1. I may be confusing something. Could someone help me out?