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A / A for a matrix is computed elementwise, and so is the undefined product of two columns #2141
Description
The wiki's Matrices page says division "will first find the inverse of the right operand", and that a multiplication whose shapes do not match does not happen. Where the operation is undefined or different, both eval and simplify instead fall back to doing it element by element:
| Input | Answer | Should be |
|---|---|---|
[[1, 2], [3, 4]] / [[1, 2], [3, 4]] |
[[1, 1], [1, 1]] |
[[1, 0], [0, 1]], as [[1, 2], [3, 4]] * [[1, 2], [3, 4]] ^ (-1) gives |
[1, 2] * [1, 2] |
[1, 4] from simplify; eval leaves it unchanged |
unchanged: a 2×1 matrix by a 2×1 matrix is undefined |
[1, 2] ^ 2 |
[1, 4] |
unchanged, for the same reason |
[1, 2] = [1, 3] |
[True, False] |
False. [1, 2] = [1, 2] gives True |
A square matrix product is right: [[1, 2], [3, 4]] * [[1, 2], [3, 4]] is [[7, 10], [15, 22]]. The elementwise branch is ExpandOnTwoArguments's (Matrix a, Matrix b) case, which every binary operation reaches when both operands have the same shape.
Found while reading Modenov's Problems in Geometry for #2131.
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