My Math Forum  

Go Back   My Math Forum > College Math Forum > Linear Algebra

Linear Algebra Linear Algebra Math Forum

LinkBack Thread Tools Display Modes
February 4th, 2010, 12:21 AM   #1
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.
typhoonss821 is offline  
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 throughout, so that the inner product is linear in the first slot and antilinear in the second.

Suppose that both satisfy for all Then,


for all

In particular, we can take to give for all Therefore
mattpi is offline  

  My Math Forum > College Math Forum > Linear Algebra

adjoint, problem

Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Problem involving adjoint and orthogonal complement walter r Linear Algebra 5 October 16th, 2013 11:57 AM
Find adjoint? rummi Linear Algebra 4 November 21st, 2012 07:51 PM
Adjoint matrix rebecca Linear Algebra 1 January 29th, 2010 07:31 AM
Rank of Adjoint BSActress Linear Algebra 0 December 14th, 2009 07:33 AM
adjoint problem meilixingqing89 Linear Algebra 2 April 9th, 2009 07:55 PM

Copyright © 2019 My Math Forum. All rights reserved.