Matrix condition number is very important because many problems are ill-conditioned and cannot be reliably solved using double precision computer systems.
Here is what I know that could happen in linear model, that the problem is ill-conditioned and R solve function cannot handle.
Case 1: using raw polynomial expansion
Case 2: using almost identical features
- Hilbert matrix is another ill-conditioned problem but less likely to see in real world.
What are other matrices that we may encounter in the linear system that are ill-conditioned?