Can <UX, UX> be written (UX)H(UX)? - A Closer Look

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SUMMARY

The discussion centers on the question of whether the expression can be represented as (UX)H(UX). Participants agree that this equivalence holds true when is defined as the dot product in real vector spaces. However, the validity of this representation depends on the specific definition of the inner product being used. If the inner product is arbitrary, the statement does not hold. The conversation references a related discussion on Physics Forums for further context.

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  • Familiarity with dot products in real vector spaces
  • Knowledge of complex conjugates and their properties
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Homework Statement


Is it true that <UX, UX> can be written (UX)H(UX)?


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The Attempt at a Solution


I think it is because <UX, UX> is equivalent to the dot product in the real case. The above would work (where H is T) if the situation was real.

It just doesn't actually say this anywhere in my notes or book, so I want to make sure I can use this fact. Thanks!
 
Physics news on Phys.org
What is your definition of <x,y>? (If it's an arbitrary inner product, then the statement isn't true. If it's a specific inner product, just use its definition to check if the statement is true).
 

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