[Numpy-discussion] Inversion of near singular matrices.

Sturla Molden sturla at molden.no
Mon Jan 31 11:27:22 EST 2011

Den 31.01.2011 03:05, skrev Algis Kabaila:
> Actually, the structural engineer
> has no interest in trying to invert a singular matrix. However
> he/she is interested (or should be interested :)  )  when the
> square response matrix might approach singularity for this would
> signal instability.

I am sorry for having confused the issue by mentioning statistics. The 
mathematics (linear algebra) is of course the same. A singular matrix 
cannot be inverted by definition. The methods mentioned (SVD, Tikohonov 
regularization), as well as the transforms mentioned by Paul, will let 
you avoid numerical instability when matrices "approach singularity" 
(i.e. are very ill-conditioned).

OT: I think I know what structural engineering is. Back in 1994 I had to 
take a class in "statikk" (not sure what that translates to in English), 
with a textbook by Fritjof Irgens. From what I remember we did vector 
calculus to ensure the forces in a construction summed to 0, so that 
Newton's first law of motion would apply. It's unhealthy to be inside a 
building otherwise ;-)

Sturla Molden

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