Orthogonality and Inner Products: Understanding a Linear Algebra Proof

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Homework Help Overview

The discussion revolves around a proof related to orthogonality and inner products in linear algebra. Participants are attempting to clarify the conditions under which the inner product of two vectors is zero.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the definitions and representations of the vectors involved, particularly \textbf{u} and \textbf{p}. There is an inquiry into the complete problem statement and whether the initial assertion about the inner product holds true for general vectors.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the problem statement and the implications of the inner product conditions. Some guidance has been offered regarding the relationship between the inner product and the norms of the vectors.

Contextual Notes

There appears to be a lack of clarity regarding the definitions of the vectors and the specific problem statement, which may be impacting the discussion.

Dustinsfl
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How to start this proof?

<u-p, p> = 0
 
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What are [itex]\textbf{u}[/itex] and [itex]\textbf{p}[/itex] supposed to represent? That statement isn't true for two general vectors [itex]\textbf{u}[/itex] and [itex]\textbf{p}[/itex].

What is the entire problem statement that you are given?
 
It has to do with inner product.
 
Is that equivalent to <u, p> - <p, p> = <u, p> - [tex]\left\|p\right\|[/tex]2
 

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