Motivation
Smith form is unique ? intrinsic property of a matrix
Graph Theory:
- Graph ? incidence matrix ? intrinsic property of graphs
Diophantine analysis: integer solutions of linear systems
Algebraic topology:
- Homology groups: gives intuition about generic structures
- can induce or refute theorems.
- Ex: Some recurring property is proven, but theorem is not valid since the computation showed that the first matrix contradict the property !