I know that the matrices {[itex]\Gamma^{A}[/itex]} obey the trace orthogonality relation [itex]Tr(\Gamma^{A}\Gamma_{B})=2^{m}\delta^{A}_{B}[/itex](adsbygoogle = window.adsbygoogle || []).push({});

In order to show that a matrix M can be expanded in the basis [itex]\Gamma^{A}[/itex] in the following way

[tex]M=\sum_{A}m_{A}\Gamma^{A}[/tex]

[tex]m_{A}=\frac{1}{2^{m}}Tr(M\Gamma_{A})[/tex]

is it enough to just substitute the first equation for M in the second, and work out that the RHS is indeed equal to [itex]m_{A}[/itex] (using the orthogonality), or is this just a mere verification, and not a proof?

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# Basis expansion

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