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My math is weak. I thought dot product measures alignment. Help me grok what "distance" means here?

• mecsred 3y ago
  Unit vectors have a normalized length, so the only difference between two unit vectors is the "heading". The angle between them can be interpreted as the the "difference" or distance, between them. Since you can compose any vector in the space out of unit vectors, you can extend the concept. See above comment inner product -> metric space.
• marginalia_nu 3y ago
  Hmm, I think I got my math wrong too. What is a proper distance function is (1 - |a*b|). That's proportional to the distance between those points on the plane spanned along the circumference of the circle/sphere/hypersphere as it's projected onto that plane.