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Archive Magazine 1996
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1994-03-26
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%OP%VS4.13 (28-Apr-92), Gerald L Fitton, R4000 5966 9904 9938
%OP%DP0
%OP%IRY
%OP%PL0
%OP%HM0
%OP%FM0
%OP%BM0
%OP%LM4
%OP%PT1
%OP%PDPipeLine
%OP%WC1018,2262,184,1748,0,0,0,0
%CO:A,72,72%
%C%Matrix Inversion
%C%by Jonathan Ormand & Gerald L Fitton
The only contribution I've has to this discussion so far is from
Jonathan Ormond. He has provided a PipeDream spreadsheet inversion
algorithm for a 4ábyá4 matrix using co-determinants. It works well. I
have included his application as the file [InvMat4] on the monthly
disc. The only time it fails is if the matrix is 'ill conditioned' (ie
when its determinant is near zero). I have searched through my memory
banks and the phrase 'pivotal condensation' came into my mind.
I think I remember using a method having that name which was reputed to
be more amenable to 'computerisation' (I hate that word)! I can't find
any notes about it but my recollection is that you extend the matrix
(to the right) with a unit matrix and then manipulate rows (adding
multiples of one row to another) until the original part of the matrix
becomes a unit matrix. My recollection, which is only half remembered,
is that, when the left half has become a unit matrix, the right hand
half of the extended matrix is the inverse of the original.