"1^(x=defective square_matrix)" does not evaluate to I(dim(x))

[Ben Abbott]

On Monday, January 14, 2008, at 12:13PM, "Rolf Fabian" <Rolf.Fabian at gmx.de> wrote:
>
>Dear Ben
>
>Thanks for checking the particular defective example using matlab.
>
>We learn that obviously matlab checks the condition number of
>the eigensystem (eigenvectors as columns of v) prior to 
>similarity (back-)transformation and displays a warning it
>v is close to singular (which means that x is defective).
>
>But I can't see why the magnitude of RCOND = 2.220446e-17
>reported by matlab differs from
>rcond = 1/cond(v) =  4.3554e-017 concluded from Octaves
>result of  "cond(v) = 2.2960e+016". Does rcond in Octave and
>MatLab have different meanings ? 
>What does ML mean by 'badly scaled?
>
>Thanks again
>
>Rolf Fabian
>

the RCOND should be compared to eps. I don't think the difference here is significant. I've noticed much larger differences between straight blas/lapack, Apple's version, and Atlas.

Regarding "badly scaled", I've always assumed one or more rows/columns contained coefficients that are scaled substantially different than the others. If I'm wrong on that,  perhaps someone else can explain.

Ben