- #1
Tio Barnabe
After reading some books on Group Theory, I have two questions on group representations (Using matrix representation) with the second related to the first one:
1 - Can we always find a diagonal generator of a group? I mean, suppose we find a set of generators for a group. Is it always possible to have at least one of them being a diagonal matrix?
2 - If so, then the eigenvectors of this diagonal operator can be used as a basis for the vector space where the representation takes place. My question is if the eigenvectors can be used or if they must be used as the basis?
1 - Can we always find a diagonal generator of a group? I mean, suppose we find a set of generators for a group. Is it always possible to have at least one of them being a diagonal matrix?
2 - If so, then the eigenvectors of this diagonal operator can be used as a basis for the vector space where the representation takes place. My question is if the eigenvectors can be used or if they must be used as the basis?