linearmap-category: Native, matrix-free linear algebra.

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.

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