working on comparison between projections

The issue is that the comparison is non-straight forward, due to the
differing storage orders in numpy and eigen, E.G., in order to give
the same result given a second-order tensor flattened as vector, the
equivalent flattened matrix representation of this

[[ 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 1. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 1. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 1.]]

becomes this

[[ 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 1. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 1. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 1.]]

I still haven't wrapped my head around why symmetry is broken by this representation