Tensor analysis takes a 3 or more dimentional space and represents each point in all dimentions
with a set of coordinates in a matrix the resulting method of calculating how spaces curve is tensor calculus and is the backbone of general relativity-matter tells space how to bend space tells matter how to move.
eigenvectors are a way of calculating vibrating forces from wave motion and as matter is both wave and particle they come in handy.
To describe the motion of wavy particles we have quantum (small amount) mechanics which only matters (im being uncontrovertial here ) at small sizes
making these 2 fit together is a major problem of physics.
