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February 4th, 2010, 12:21 AM | #1 |
Newbie Joined: Feb 2010 Posts: 1 Thanks: 0 | Adjoint problem
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 function 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 ? Is it right to mimic the textbook which discuss the problem at the condition of T 's being an operator ? Last edited by skipjack; November 4th, 2016 at 08:18 AM. |
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February 6th, 2010, 06:11 AM | #2 |
Senior Member Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0 | Re: Adjoint problem
I'll pretend to be a pure functional analyst ![]() Suppose that so for all EDIT: In particular, we can take |
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