Given a real nxn symmetric and non-positive definite matrix,. .

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Discussion Overview

The discussion revolves around the properties of a real nxn symmetric and non-positive definite matrix, specifically examining whether the expression (x^TBx)^1/2 qualifies as a norm on R^n. The scope includes theoretical exploration and mathematical reasoning related to the definition of norms.

Discussion Character

  • Exploratory, Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant proposes that (x^TBx)^1/2 should be shown not to be a norm on R^n.
  • Another participant suggests checking if the expression satisfies all the requirements for a norm.
  • A different participant expresses uncertainty about how to approach the problem, indicating a lack of understanding of the necessary checks.
  • Another reply advises reading the definition of "norm" to determine if the expression meets the criteria.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on how to approach the problem, with some expressing uncertainty and others suggesting methods for verification.

Contextual Notes

There is a lack of clarity on the specific requirements for a norm that need to be checked, and the discussion does not resolve how to apply these requirements to the given expression.

kholden
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let B be a nXn real symmetric and non-positive definite matrix. Show that (x^TBx)^1/2 is not a norm on R^n.
 
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Check to see if it satisfies all the requirements for a norm.
 
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how do you check o? i honestly have no idea how to do the problem.
 
Read the definition of "norm" and check to see if this satisfies it.
 

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