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## Homework Statement

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].

## 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), and

*n*real 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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