Seonglae ChoGeneralized and abstracted structure of Linear Independent
Matroid abstracts and generalizes the notion of linear independence in vector spaces. A matroid is a structure that can be defined in many equivalent ways, including in terms of independent sets, bases or circuits, rank functions, closure operators, and closed sets or flats.
There are some standard ways to make new matroids out of old ones, including duality.
- Independency
- Basis
Matroid Notion
Matroid
In combinatorics, a branch of mathematics, a matroid /ˈmeɪtrɔɪd/ is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid axiomatically, the most significant being in terms of: independent sets; bases or circuits; rank functions; closure operators; and closed sets or flats. In the language of partially ordered sets, a finite simple matroid is equivalent to a geometric lattice.
https://en.wikipedia.org/wiki/Matroid