The term *numerical linear algebra* is often used almost
synonymous with *matrix modifications*. However, what's interesting
for most applications are really just *points in some vector space*
and linear mappings between them, not matrices (which represent
points or mappings, but inherently depend on a particular choice
of basis / coordinate system).

This library implements the crucial LA operations like solving
linear equations and eigenvalue problems, without requiring
that the vectors are represented in some particular basis. Apart
from conceptual elegance (only operations that are actually
geometrically sensible will typecheck – this is far stronger than
just confirming that the dimensions match, as some other libraries
do), this also opens up good optimisation possibilities: the
vectors can be unboxed, use dedicated sparse compression, possibly
carry out the computations on accelerated hardware (GPU etc.).
The spaces can even be infinite-dimensional (e.g. function spaces).

The linear algebra algorithms in this package only require the
vectors to support fundamental operations like addition, scalar
products, double-dual-space coercion and tensor products; none of
this requires a basis representation.