(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let [tex]V[/tex] be the [tex]\mathbb{R}[/tex]-vector space [tex]\mbox{Herm}_n( \mathbb{C} )[/tex]. Find [tex]\dim_{\mathbb{R}} V[/tex].

3. The attempt at a solution

I'd say the dimension is [tex]2n(n-1)+n=2n^2-n[/tex], because all entries not on the main diagonal are complex, so you have [tex]n(n-1)[/tex] entries which you have to split up in two (the scalars are real), andnreal entries on the main diagonal (which you don't have to split up in two). However, the paper I have says that [tex]\dim_{\mathbb{R}} V[/tex] is equal to [tex]n^2[/tex]. I can't see how that could be correct. Have I misunderstood something?

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# Homework Help: Basis of a real hermitian matrix vector space with complex entries

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