I'm writing up some notes on matrices for my students and ran into this
inconsistency (I think). I start by creating a matrix and augment its
transpose, just to have a non-square matrix:
A=Matrix([[3,1],[-1,2]])
B=A.transpose()
C=A.augment(B)
Now if I ask for the echelon form of C, I get this result, which isn't
fully reduced:
C.echelon_form()
[1 5 5 3 ]
[0 7 6 5 ]
That's fine because
C.parent()
Full MarixSpace of 2 by 4 dense matrices over Integer Ring
But I would expect that the inverse of A wouldn't be computed under this
condition, but
A.inverse()
[ 2/7 -1/7 ]
[1/7 3/7 ]
Is there a logical reason why this happens?
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