# B Matrices of su(3) and sphere symmetry

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1. Oct 31, 2016

### 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 cant 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..

2. Oct 31, 2016

### Staff: Mentor

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 $\mathfrak{su}(3)$.

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