In this question I let "x1t , x2t, x3t " be the conjugate of x1, x2, x3(adsbygoogle = window.adsbygoogle || []).push({});

The hermitian form

Hc(x) = c*x1t*x1 + 2*x2t*x2 - i*x1t*x2 + i*x2t*x1 + x1t*x3 + x3t*x1

+i*x2t*x3 - i*x3t*x2 (sorry, it`s a bit messy)

For which value of c is Hc ositive definite?

I have tried to find the eignvalue in terms of c by trying to solve the

charactiristic polynomial, but seems too complicate to do, I`ve also tried

to solve by completing the square but not so successful.

So is there any way to solve this without using computer softwares like

maple? Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A positive definite Hermitian Form

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**