Matrices of su(3) and sphere symmetry

[kimcj]

i used to get pauli matrices by the following steps
it uses the symmetry of a complex plane sphere i guess so..?
however i can't get the 8 gell mann matrices
please help !

method*: (x y) * (a b / c d ) = (x' y')
use |x|^2 + |y|^2 = |x'|^2 + |y'|^2
and |x| = x * x(complex conjugate)

this way i can get 3 pauli matrices
however can't apply them to su(3) ones..

 

[fresh_42]

The Pauli matrices are elements of $SU(2)$ and span $\mathfrak{su}(2)$. A (random) coincidence.

The Gell-Mann matrices are not elements of $SU(3)$. They span $\mathfrak{su}(3)$.