If we have an equation that looks like $$H=Y$$ and we want to multiply H by either $$ReM_{IJ}$$ or $$ImM_{IJ}$$ where $$M_{IJ}$$ is a complex matrix. But the thing is that $$Y=\star(...)$$ where $$\star$$ is hodge star and (...) is set of complex functions and other numerical stuff, my question is technical here, say we decide to multiply H by $$ReM_{IJ}$$ can we move $$ReM_{IJ}$$ into the parenthesis and jump over the Hodge star? That is to say $$ReM_{IJ}H=\star(ReM_{IJ} ...)$$ or this is absolutely wrong and we should keep $$ReN_{IJ}$$ outside the Hodge star? That is to say $$ReM_{IJ}H=ReM_{IJ}\star( ...)$$(adsbygoogle = window.adsbygoogle || []).push({});

EDIT: M_{IJ} is a complex matrix

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# A technical question that has to do with Hodge Star

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