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Applying a lambda to a vector treats the vector as a number #2132
Description
Applying a lambda to a vector gives a matrix of vectors where it should multiply:
| Input | Answer | Should be |
|---|---|---|
apply(lambda(u, [[0, -1], [1, 0]] * u), [p, q]) |
[[0, [-p, -q]], [[p, q], 0]] |
[-q, p] |
apply(lambda(u, [1, 1]T * u), [p, q]) |
[[[p, q], [p, q]]] |
p + q |
Written out, [[0, -1], [1, 0]] * [p, q] simplifies to [-q, p]. The body on its own, [[0, -1], [1, 0]] * u, simplifies to [[0, -u], [u, 0]]. That is right when u is a number, and the answer is that matrix with the vector put in for u.
Found while reading Modenov's Problems in Geometry for #2131, where this lambda is the book's rotation of a plane vector through π/2. Related: #495.
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