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- #1

- Feb 5, 2012

- 1,621

Here's a problem I encountered. I think there's a mistake in this problem.

**Problem:**

Let \(f:\,V\times V\rightarrow\mathbb{C}\) be a Hermitian function (a Bilinear Hermitian map), \(q:\, V\rightarrow\mathbb{C}\) be given by \(q(v)=f(v,\,v)\). Prove that following,

\[4f(x,\,y)=q(x+y)-q(x-y)+iq(x+iy)-iq(x-iy)\]

When I find the answer I get,

\[q(x+y)-q(x-y)+iq(x+iy)-iq(x-iy)=0\]

I would be really grateful if someone can confirm my answer.