Re: Inverse Matrix Function appears a bit wonky

[Henry F. Mollet]

Michael probably can give us the solution for a 4x4 with numbers between
1-10. I run the following 10 times and always got rank = 4.
octave:3> ceil(10*rand(4))
ans =

   4   1   5   5
   1   2   1   1
   3   9  10   6
   7   5   6   9

octave:4> rank(ans)
ans = 4
Henry




on 11/5/04 1:31 AM, Michael Creel at address@hidden wrote:

> For 2x2 matrices made up of integers between -3 and +3, the answer is
> obviously 14.4%. If you can't see that at first sight, try running the
> attached script. Sheesh!
> Michael
> 
> On Thursday 04 November 2004 16:33, Przemek Klosowski wrote:
>>    Your arbitrary test matrix is ill-conditioned so any attempt to invert
>>    ...
>>    accuracy. For another example, try hilb(n) * inv(hilb(n)) for n = 1,
>>    2, ..., 15. The Hilbert matrix is famously illconditioned for large n.
>> 
>> it is so frequent that it's even funny: people come up with a random
>> small-dimension matrix, typically made up of smallish integers, and
>> get a singular one. Does anyone know how dense is the set of singular
>> matrices in the set of all small-size, small-value matrices? is it
>> really that dense, or are we having bad luck :)?
>> 
>>        p
>> 
>> 
>> 
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