I worry that this tweet will be wildly unpopular, I do, but I must press on: Does anyone out there have a plain-English, intuitive definition of "linear transformation"?
-
Linear transformations can move a rectangle around, rotate it, stretch it or scale it, distort it into a parallelogram, but never bend the edges
Nice. Like this one from @3blue1brown: https://twitter.com/Grinkenschmied/status/1187090807133786114 … Funny, the line-based definition is simpler, but I like the concreteness of the rectangle-based explanation. Leaves a little open what happens to the origin, though.
-
-
Projective transformations preserve lines and can also fix the origin, but are non-linear. Linear transformations have the additional property of preserving parallelism
-
Diagonal lines will end up curved in a projective transformation.pic.twitter.com/aP22hB4gn5
- 2 more replies
New conversation -
-
-
How about transformations where non-lines remain non-lines?
-
Ah, the sweet smell of definition-by-complementarity in the morning.
- 1 more reply
New conversation -
-
-
Perhaps it'd help to mention panning vs. zooming on a phone, re: the origin.
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.