Linear Algebra, unique minimizer of a quadratic function

[kristo]

Homework Statement

The part I'm having problems with is where the last two expressions in 4.13 are equated. Why is x^tKx*equal to x^{*^t}Kx*?

The Attempt at a Solution

x^tKx* is an inner product and due to symmetry is equal to x^{*^t}Kx, but wouldn't equating x to x* mean every <x,y> = <x,x> = <y,y>?

Many thanks if someone decides to help me out.

 

[haruspex]

Why is x^tKx*equal to x^{*^t}Kx*?

That's not what happened. Try multiplying out the left hand expression of the second line of 4.13.