This is fixed (sort of) in R-1.8.0 which explicitly says that the det
function does not handle complex matrices.
> m = matrix(complex(re=rnorm(9),im=rnorm(9)),3,3)
> det(m)
Error in determinant.matrix(x, logarithm = TRUE, ...) :
determinant not currently defined for complex matrices
R.P.P.P.Grasman@uva.nl writes:
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> Hello,
>
> When I use det() and qr() on complex matrices the result is in some >
cases indeterministic. The documentation speaks of numeric matrices (and >
not of complex matrices) but det() uses qr() which should handle complex >
matrices correctly. I've also tried using only qr() with=20
>
> similar results. det() returns a value that is not the determinant of >
the complex matrix (in accordance with documentations limitation to > numeric
matrices), whereas the product of the eigenvalues obtained with > eigen()
does evaluate to the determinant of the matrix.
>
> To repeat the error in a simple as possible example I did the following:
>
> I freshly started R without loading any previously stored image.
>
> > m =3D matrix(complex(re=3Drnorm(9),im=3Drnorm(9)),3,3) # multiple
> m's were tried
> > m
> [,1] [,2] [,3]
> [1,] -0.56135706+0.9346292i 0.3626032+0.73012622i -0.6629864+0.9328771i
> [2,] -0.05999599-0.6931185i -1.4558785+0.66410894i 0.8503606-1.0104882i
> [3,] -1.29420594-1.0878549i 0.7834801+0.01872038i -0.6378357-0.6318547i
>
> > y =3D sapply(1:10000,function(i) det(m)); plot.ts(y) # may need >
repetition
> > var(y)
> [1] 3.940272
>
> The plot shows that the sign of det alternates indeterministically (at >
least for some m generated this way, like the m attached in the m.RData >
file).
>
> I note that a similar problem was reported in >
http://www.r-project.org/nocvs/mail/r-devel/2002/0139.html but I >
couldn't find a report of this particular problem.
>
> I would suggest to make det compatible with complex matrices, or at >
least give a warning.
>
> Regards,
>
> Raoul
>
> --please do not edit the information below--
>
> Version:
> platform =3D i386-pc-mingw32
> arch =3D i386
> os =3D mingw32
> system =3D i386, mingw32
> status =3D=20
> major =3D 1
> minor =3D 6.2
> year =3D 2003
> month =3D 01
> day =3D 10
> language =3D R
>
> Windows 2000 Professional (build 2195) Service Pack 4.0
>
> Search Path:
> .GlobalEnv, package:ctest, Autoloads, package:base
>
>
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> Raoul Grasman=20
> Dept. Psychology, University of Amsterdam,=20
> Roetersstraat 15,=20
> NL-1018WB Amsterdam,=20
> the Netherlands=20
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--
Douglas Bates bates@stat.wisc.edu
Statistics Department 608/262-2598
University of Wisconsin - Madison http://www.stat.wisc.edu/~bates/