Hello. Consider the following matrix:
mp <- matrix(c(0,1/4,1/4,3/4,0,1/4,1/4,3/4,1/2),3,3,byrow=T) > mp [,1] [,2] [,3] [1,] 0.00 0.25 0.25 [2,] 0.75 0.00 0.25 [3,] 0.25 0.75 0.50 The eigenvectors of the previous matrix are 1, 0.25 and 0.25 and it is not a diagonalizable matrix. When you try to find the eigenvalues and eigenvectors with R, R responses: > eigen(mp) $values [1] 1.00 -0.25 -0.25 $vectors [,1] [,2] [,3] [1,] 0.3207501 1.068531e-08 -1.068531e-08 [2,] 0.4490502 -7.071068e-01 -7.071068e-01 [3,] 0.8339504 7.071068e-01 7.071068e-01 The eigenvalues are correct but the eigenvectors aren't. Moreover, if you try to compute the inverse of the matrix of eigenvectors, R is not aware that this matrix is singular: > solve(eigen(mp)$vectors) [,1] [,2] [,3] [1,] 6.235383e-01 6.235383e-01 6.235383e-01 [2,] 3.743456e+07 -9.358641e+06 -9.358640e+06 [3,] -3.743456e+07 9.358640e+06 9.358641e+06 My question is: how can I fix it? Arnau. ------------------------------------------------------------ Arnau Mir Torres Edifici A. Turmeda Campus UIB Ctra. Valldemossa, km. 7,5 07122 Palma de Mca. tel: (+34) 971172987 fax: (+34) 971173003 email: arnau....@uib.es URL: http://dmi.uib.es/~arnau ------------------------------------------------------------ [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.