Sorry for any typos, typed on phone:

To avoid any further confusion I think the matrix you're trying to build is the 
Vertex' tangent-space matrix. 

These are per-vertex as opposed to per object like he local matrix.

So what you'd do is retrieve the "delta" in tangent-space of and re-apply that 
delta on the other mesh.

Note that a Vertex' position multiplied by its own inverse matrix would always 
be zero since its tangent-space matrix is based on its own position.

What I think you're trying to do is create Tangent-space blendshapes.

Basically you create the delta by having two meshes and store the delta:

delta = blendshapePt * tangentSpace.inverse()

And then apply that delta to another mesh's point in that vertex' tangent space:

targetPt += delta * targetTangentSpace

Not sure about the order of matrix multiplication here, I always tend to mess 
it up in Maya when doing it out the top of my head.

Cheers,
Roy

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