Tuesday, 4 March 2025

Coding with Bilinear Maps

When Pycryptonistas advance beyond the familiar realm of linear algebra to the new realm of multilinear algebra there are terms that must be mastered post haste to make sense of the new environs.

Amongst these terms is the term bilinear map a simple sounding term but oddly not widely socialised even among linear algebra aficionados.

A bilinear map is a function that combines elements of two vector spaces to yield an element of a third vector space, and is linear in each of its arguments. Matrix multiplication is an example.

To be confident in bilinear maps you should be able to product multiple examples of bilinear maps from basic mathematics.