I recently teach myself linear algebra with Friedberg's textbook.
And I have a question about adjoint operator, which is on p.367.
Definition Let T : V → W be a linear transformation where V and W are finite-dimensional inner product spaces with inner products <‧,‧> and <‧,‧>' respectively. A funtion T* : W → V is called an adjoint of T if <T(x),y>' = <x,T*(x)> for all x in V and y in W.
Then ,my question is how to prove that there is a unique adjoint T* of T ?
Can anyone give me some tips ? thanks^^