Q20 exam 2018

Hello,

The question was TF "The triangle inequality and homogeneity of a norm together imply that any norm is convex"

What is norm homogeneity ? I don't remember that concept anywhere from the course.

Thank you for your help

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I think that this is the scaling property, i.e. \( ||\lambda x || = | \lambda | ||x|| \) for any scalar \( \lambda \).

||ax|| = |a| * ||x|| , a is scalar

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Top comment

I think that this is the scaling property, i.e. \( ||\lambda x || = | \lambda | ||x|| \) for any scalar \( \lambda \).

When i was doing this question, i was wondering if the "any norm" property holds true. The lectures specified for norms that in R^d that this holds. Does it actually hold for any and all norms?

Yes since any norm has these 2 properties (https://en.wikipedia.org/wiki/Norm_(mathematics)).

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