Abstract Algebra: Schwarz Inequality Homework

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Homework Help Overview

The discussion revolves around understanding a specific equation related to the proof of the Schwarz inequality in abstract algebra. Participants are examining the correctness of an equality in the context of norms and dot products.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster questions the validity of an equality in the equation, suggesting it should be an inequality instead. Other participants assert that the equality is indeed correct, referencing the use of the dot product in the context of norms.

Discussion Status

The discussion is ongoing, with some participants providing clarification on the correctness of the equation. There appears to be a divergence in understanding, as the original poster expresses doubt while others confirm the equality.

Contextual Notes

Participants are navigating the nuances of the Schwarz inequality and its proof, indicating a potential gap in foundational understanding or assumptions regarding the properties of norms and dot products.

icystrike
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Homework Statement


This is part of the proof of Schwarz inequity.
Please help me understand the following equation , i think it should not be a equal sign instead it should be greater or equal to.

attachment.php?attachmentid=24531&stc=1&d=1269158428.jpg


Homework Equations





The Attempt at a Solution

 

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will someone clear my doubt ? thanks in advance
 
No - the equals is correct. The norm is taken by multiplying out using the dot product (so a x b = aTb).
 
mrbohn1 said:
No - the equals is correct. The norm is taken by multiplying out using the dot product (so a x b = aTb).

Thanks mrbohn. (:
 

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