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**typhoonss821** 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^^