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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

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  • 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?

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  • $\begingroup$ I am sorry, but the code given (in which language ?) is impossible for me to understand. $\endgroup$ – Jean Marie Aug 4 '16 at 15:21
  • $\begingroup$ He mentions it is using "R". $\endgroup$ – Moo Aug 4 '16 at 18:31
  • $\begingroup$ sorry, I originally asked this question in statistics community and got closed, so I asked here. The code is just generate some random matrix, use polynomial expansion / generate similar columns, and calculate condition number. $\endgroup$ – hxd1011 Aug 4 '16 at 20:47

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