Orthogonality and Inner Products: Understanding a Linear Algebra Proof

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SUMMARY

The discussion centers on the proof involving orthogonality and inner products in linear algebra, specifically addressing the relationship between vectors u and p. The statement = 0 is clarified as not universally true for arbitrary vectors u and p. Participants emphasize the need to understand the full problem statement related to inner products, particularly the expression - = - ||p||², which is crucial for establishing the proof.

PREREQUISITES
  • Understanding of linear algebra concepts, specifically inner products.
  • Familiarity with vector notation and operations.
  • Knowledge of orthogonality in vector spaces.
  • Basic proficiency in mathematical proofs and logic.
NEXT STEPS
  • Study the properties of inner products in vector spaces.
  • Explore the concept of orthogonality and its implications in linear algebra.
  • Learn how to construct and analyze mathematical proofs in linear algebra.
  • Investigate the relationship between inner products and vector norms.
USEFUL FOR

Students and educators in mathematics, particularly those focusing on linear algebra, as well as researchers and professionals needing a deeper understanding of vector relationships and proofs involving inner products.

Dustinsfl
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How to start this proof?

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

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> - \left\|p\right\|2
 

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