Linear Algebra operators follow from the definition (i.e. all Linear Algebra functions can be derived from addition and scalar multiplication)…
rotations can be implemented as two reflections or [three shears](https://www.ocf.berkeley.edu/~fricke/projects/israel/paeth/rotation_by_shearing.html#:~:text=To%20do%20a%20shear%20operation%20on%20a%20raster%20image%20(that,from%20the%20rotation%20angle%20%CE%98.).
the toffoli gate is one of the universal reversible logic gates.
http://jdh.hamkins.org/the-hierarchy-of-logical-expressivity/
Hasse diagram, ordered by expressivity, of all equivalence classes of sets of binary logical operations
- Generalizing, Post’s lattice is roughly a hierarchy of all logic operations on any number of arguments