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