Hi, this question seem to fall somewhere between Analysis and Algebra;(adsbygoogle = window.adsbygoogle || []).push({});

I just choose this section; sorry if it is the wrong one. I would appreciate

any suggestions, refs., etc.

I'm basically trying to see if the different definitions of adjoint

maps can be unified into a single definition:

1) Adjoint of a linear map: given a linear map L:V-->W between f.d

vector spaces V,W , the adjoint map L*: W*-->V* is given by, for w* in W*,

for v in V :

L*[(w*)(v)]:=w*(L(v)).

2) Given an inner-product space (V, < ,>) , and a linear map L:V-->V,

the adjoint L* (which may not exist if V is infinite-dimensional) is

defined as L* satisfying:

<Lv,w>=<v,L*w>

for any v,w in V.

Can these two definitions of adjoint be unified into a single, broader

definition of adjoint map?

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# Unifying Different Definitions of Adjoint Map

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