Singletons, Vexels, and the Rank of a Maxel - Data Structures in Mathematics

Explore the concept of vexels and their relationship to maxels in this 28-minute mathematics lecture. Delve into the multiset framework used to set up maxel theory and its one-dimensional analog for structuring vector space theory. Learn about singletons, the interpretation of maxel-vexel multiplications, and how vexels can be viewed as multisets. Examine friezes, vectors as representations of vexels, and the hierarchy of linear spaces. Conclude with an introduction to the rank of a maxel, gaining valuable insights into advanced mathematical structures and their applications in linear algebra and geometry.

Intro to vexels
Maxels with just one row/column
Interpretations of maxel vexel multiplications
Singletons
Vexels are Msets
A frieze
A vector considered as a picture of a vexel
'Hierarchy' of linear spaces
The rank of a maxel