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Not quite sure what you mean but now I agree with your previous point that the coordinate system is irrelevant because these normal derived Lp metrics can be sp
by srean 1y ago
Not quite sure what you mean but now I agree with your previous point that the coordinate system is irrelevant because these normal derived Lp metrics can be specified in a coordinate free way just by specifying their unit ball set
- shiandow 1y agoWel what does it mean to be orthogonal? I'd argue that if you only have a metric then a line (segment) is orthogonal to some set if it is the shortest path from a point to a set. For norms it should work to only consider straight lines. What I was getting at is that the x and y grid is orthogonal for all Lp norms. The interesting stuff happens if you pick a different line as x-axis. Orthogonal projection to a different axis still works though, the resulting grid just won't be orthogonal in the conventional sense.