# Matroids

Matroids are an abstraction of Vector Spaces.  Vectors spaces have addition and scalar multiplication and the axioms of vectors spaces lead to the concepts of subspaces, rank, and independent sets.  All Vector Spaces are Matroids, but Matroids only retain the properties of independence, rank, and subspaces. The idea of the Matroid closure of a set is the same as the span of the set in the Vector Space.

1. Thanks for reminding me of these. It has been a long time and matroids are quite interesting.

2. I’m not very familiar with them, but I started seeing them in the compressed sensing community (see e.g. “Sublinear Compressive Sensing (CS) and Support Weight Enumerators of Codes: A Matroid Theory Approach“), so I’ve started looking at them.  I have done a lot of work on linear projections (idempotent, self-adjoint matricies), so I wonder if that theory carries over to Matroids in some way.