So i have a four dimensional complex vector space ( L+ix , L+iy, L+iz, L+ig) can i choose a standard basis for it for ex: imagine that this are columns not rows ->
L+ix(1,0,0,0) + L+iy(0,1,0,0)+ L+iz(0,0,1,0)+ L+ig(0,0,0,1)=( L+ix , L+iy, L+iz, L+ig)
or they has to be a certain one?