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The post contains no geometry. Which is the only worthwhile content of dot products. Explaining the dot product by its implementation over R^n is pointless. Co

• tptacek 1y ago
  The only worthwhile content of dot products is geometry?
  • nh23423fefe 1y ago
    of course. dot products are a symmetric form on vector spaces. they let you compute the spheres of radius r. given the sphere of radius r, for any pair of vectors v,w in the sphere -r^2 <= dot(v,w)=dot(w,v) <= r^2 as w varies from v to -v the value moves from r^2 through 0 to -r^2 this is how we define parallel perpendicular and antiparallel. the dot product is only meaningful in a geometric context. by definition it projects vectors down to scalars. fixing the scalar value finds the spheres, and for a sphere we can vary the vectors to compute cosines.