I have the following problem: I try to make the spectral decomposition for the following matrix by utilising the function eigen. 0.4015427 0.08903581 -0.2304132 0.08903581 1.60844812 0.9061157 -0.23041322 0.9061157 2.9692562 When checking the result I was not able to produce the original matrix by using the decomposition. It also appears that the product T''T, where T is a matrix of eigenvectors, is not an identity matrix. Tapio Nummi University of Tampere -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
On Mon, 22 Jan 2001, Tapio Nummi wrote:> > I have the following problem: > > I try to make the spectral decomposition > for the following matrix by utilising the > function eigen. > > 0.4015427 0.08903581 -0.2304132 > 0.08903581 1.60844812 0.9061157 > -0.23041322 0.9061157 2.9692562 > > When checking the result I was not able > to produce the original matrix by using > the decomposition. It also appears that > the product T''T, where T is a matrix of > eigenvectors, is not an identity matrix.Did your version of R pass make check? Some compilers have trouble with eigen, so try example(eigen). And *PLEASE* give your R version and platform. On mine (1.2.1, Solaris)> sm <- eigen(m, sym=TRUE) > sm$values [1] 3.4311626 1.1970027 0.3510817 $vectors [,1] [,2] [,3] [1,] -0.05508142 -0.2204659 0.9738382 [2,] 0.44231784 -0.8797867 -0.1741557 [3,] 0.89516533 0.4211533 0.1459759> V <- sm$vectors > t(V) %*% V[,1] [,2] [,3] [1,] 1.000000e+00 -1.665335e-16 -5.551115e-17 [2,] -1.665335e-16 1.000000e+00 2.428613e-16 [3,] -5.551115e-17 2.428613e-16 1.000000e+00> V %*% diag(sm$values) %*% t(V)[,1] [,2] [,3] [1,] 0.40154270 0.08903581 -0.2304132 [2,] 0.08903581 1.60844812 0.9061157 [3,] -0.23041320 0.90611570 2.9692562 I reckon you have a broken installation. -- Brian D. Ripley, ripley at stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272860 (secr) Oxford OX1 3TG, UK Fax: +44 1865 272595 -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
On Mon, 22 Jan 2001, Tapio Nummi wrote:> I try to make the spectral decomposition > for the following matrix by utilising the > function eigen. > > 0.4015427 0.08903581 -0.2304132 > 0.08903581 1.60844812 0.9061157 > -0.23041322 0.9061157 2.9692562 > > When checking the result I was not able > to produce the original matrix by using > the decomposition. It also appears that > the product T''T, where T is a matrix of > eigenvectors, is not an identity matrix.Hi Tapio, I''m not having your problems:> A[,1] [,2] [,3] [1,] 0.40154270 0.08903581 -0.2304132 [2,] 0.08903581 1.60844812 0.9061157 [3,] -0.23041320 0.90611570 2.9692562> sdec <- eigen(A, symm=TRUE)> t(sdec$vectors) %*% sdec$vectors[,1] [,2] [,3] [1,] 1.000000e+00 -1.665335e-16 -5.551115e-17 [2,] -1.665335e-16 1.000000e+00 2.428613e-16 [3,] -5.551115e-17 2.428613e-16 1.000000e+00> sdec$vectors %*% diag(sdec$values) %*% t(sdec$vectors) - A[,1] [,2] [,3] [1,] -5.551115e-17 -2.775558e-17 2.000000e-08 [2,] -5.551115e-17 1.998401e-15 8.881784e-16 [3,] -1.387779e-16 7.771561e-16 2.220446e-15 Cheers, Jonathan. Jonathan Rougier Science Laboratories Department of Mathematical Sciences South Road University of Durham Durham DH1 3LE tel: +44 (0)191 374 2361, fax: +44 (0)191 374 7388 http://www.maths.dur.ac.uk/stats/people/jcr/jcr.html -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
> I try to make the spectral decomposition > for the following matrix by utilising the > function eigen. > > 0.4015427 0.08903581 -0.2304132 > 0.08903581 1.60844812 0.9061157 > -0.23041322 0.9061157 2.9692562 > > When checking the result I was not able > to produce the original matrix by using > the decomposition. It also appears that > the product T''T, where T is a matrix of > eigenvectors, is not an identity matrix.- I think that a couple of people have reported problems with eigen, that were actually traceable to their BLAS, but I can''t now find the messages in the archive, so I may be mis-remembering. Simon ______________________________________________________________________> Simon Wood snw at st-and.ac.uk http://www.ruwpa.st-and.ac.uk/simon.html > The Mathematical Institute, North Haugh, St. Andrews, Fife KY16 9SS UK > Direct telephone: (0)1334 463799 Indirect fax: (0)1334 463748-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
Need to set the symmetry argument. Say x = the matrix eigen(x,sym=T) At 06:33 PM 1/22/01 +0300, Tapio Nummi wrote:> >I have the following problem: > >I try to make the spectral decomposition >for the following matrix by utilising the >function eigen. > > 0.4015427 0.08903581 -0.2304132 > 0.08903581 1.60844812 0.9061157 >-0.23041322 0.9061157 2.9692562 > >When checking the result I was not able >to produce the original matrix by using >the decomposition. It also appears that >the product T''T, where T is a matrix of >eigenvectors, is not an identity matrix. > > Tapio Nummi > University of Tampere > >-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.->r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html >Send "info", "help", or "[un]subscribe" >(in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch >_._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._>Yudi Pawitan yudi at stat.ucc.ie Department of Statistics UCC Cork, Ireland Ph 353-21-490 2906 Fax 353-21-427 1040 -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
On Mon, 22 Jan 2001, Simon Wood wrote:> > I try to make the spectral decomposition > > for the following matrix by utilising the > > function eigen. > > > > 0.4015427 0.08903581 -0.2304132 > > 0.08903581 1.60844812 0.9061157 > > -0.23041322 0.9061157 2.9692562 > > > > When checking the result I was not able > > to produce the original matrix by using > > the decomposition. It also appears that > > the product T''T, where T is a matrix of > > eigenvectors, is not an identity matrix. > > - I think that a couple of people have reported problems with eigen, that > were actually traceable to their BLAS, but I can''t now find the messages > in the archive, so I may be mis-remembering. >There was a problem at one time with AIX systems, apparently due to C/Fortran compatibility issues. I think it has been resolved, though we have only tested a few C/Fortran compiler combinations. -thomas Thomas Lumley Asst. Professor, Biostatistics tlumley at u.washington.edu University of Washington, Seattle -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._