[Numpy-discussion] Inversion of near singular matrices.
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 ;-)
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