Hello everyone!
I noticed that powers of non-square matrices (with MatPow) do not raise an
error, e.g. if A = MatrixSymbol('A', 2, 3) then MatPow(A, 10) does not
raise. I would assume that this is just an oversight, but then I see
explicit unit tests for MatPow(A, 1), which make me wonder if perhaps there
is a reason this is supported. However the behavior is not consistent,
since A ** 1 does raise an error anyway. But then again ZeroMatrix(2, 3) **
1 does not raise.
As far as I know most textbooks do not define A ** n at all for any value
of n when A is not square. This might also be of interest:
https://math.stackexchange.com/questions/101590/what-is-zero-power-of-a-non-square-matrix
So question: Would it be an acceptable breaking change to completely forbid
powers of non-square matrices, including the barely useful MatPow(A, 0) and
MatPow(A, 1)? It doesn't seem to break any tests (other than
test_matpow.py).
Background: I plan to do some clean-up in the MatPow code to make it follow
the same convention used in other places, e.g. move the argument validation
from MatrixExpr.__pow__() to MatPow.__new__() and move some specialized
code from MatPow.doit() to the _eval_power() methods of respective
sub-classes.
Thanks!
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