Matrix rivet setup
So, the way matrices work in Maya is that the first three rows of the matrix describe the X, Y and Z axis and the fourth row is the position.
What this means to us, though, is that if we have two vectors and a position we can always construct a matrix out of them, since the cross product of the two vectors will give us a third one. So here is how our matrix construction looks like in the graph.
You can choose either tangentU or tangentV for the second axis; refer to this.
Even simpler, you can use tangentV as the third vector, although this might break orthogonality. Here, decomposeMatrix could filter out any shearing from the matrix.