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That’s not mathematically accurate though, is it? We haven’t reduced the dimension of the vector by one. Pray tell, which dimension do we lose when we normaliz
by extasia 2y ago
That’s not mathematically accurate though, is it? We haven’t reduced the dimension of the vector by one.
Pray tell, which dimension do we lose when we normalize, say a 2D vector?
- deleted 2y ago[deleted]
- thaumasiotes 2y agoMagnitude, obviously. >>> Magnitude is not a dimension [...] To prove this normalize any vector and then try to de-normalize it again. Say you have the vector (18, -5) in a normal Euclidean x, y plane. Now project that vector onto the y-axis. Now try to un-project it again. What do you think you just proved?
- creata 2y agoMathematically, it's fine to say that you've lost the magnitude dimension. Before normalization, the vector lies in R^n, which is an n-dimensional manifold. After normalization, the vector lies in the unit sphere in R^n, which is an (n-1)-dimensional manifold.
- langcss 2y agoA circle circumference is a line, is 1D?