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In (Vaz and da Rocha, 2016;pg108) the following two step process is given for finding the matrix representation of a Clifford algebra: (verbatim; except for notation)

(1) Choose a set of $N$ primitive idempotents $f_A$ ($A=1,...,N$) of $\mathscr{C}{l}_{p,q}$ such that $\sum_A f_A=1$, with one of them being a primitive idempotent, for instance $f_1$.

(2) Choose elements $\{\mathscr{E}_{A1}\}$ and $\{\mathscr{E}_{1a}\}$ ($A=1,...,N$) such that $f_1=\mathscr{E}_{1A} \mathscr{E}_{A1}$ and that eqn (4.43) holds, namely, $f_B\mathscr{E}_{A1}=\delta_{AB}\mathscr{E}_{A1}$ and $\mathscr{E}_{1A}f_B=\delta_{AB}\mathscr{E}_{1A}$.

I am confused by the first point; Do all my $f_A$'s need to be primitive or just one of them?

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  • $\begingroup$ Might Mathematics be better suited for this math question? $\endgroup$ – Kyle Kanos Aug 30 '17 at 11:14
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    $\begingroup$ @KyleKanos I am not sure. Math SE doesn't even have a 'spinor' tag and since Spinors (a concept used more in physics then in maths) are defined using Clifford algebras I thought it best to post it here - although I might be wrong and am happy for it to be migrated to MSE. $\endgroup$ – Quantum spaghettification Aug 30 '17 at 11:20
  • $\begingroup$ This question was 1 close vote short of a full migration to Mathematics. Note that the Phys.SE community usually welcomes math questions relevant for physics. I closed it as H&E to buy the Phys.SE community more time to decide what to do. $\endgroup$ – Qmechanic Sep 1 '17 at 9:03
  • $\begingroup$ @Quantumspaghettification Your question as stated does not refer to spinor tags... or maybe we need to read the reference to get the connection with spinors? $\endgroup$ – ZeroTheHero Sep 2 '17 at 19:42