- Thread starter
- #1
- Feb 5, 2012
- 1,621
Hi everyone,
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.
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.