search for: diagonalizable

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...

...2] [,3] > [1,] 8.788496e-09 1.000000e+00 1 > [2,] 3.000000e+00 -9.313226e-10 1 > [3,] 1.000000e+00 3.000000e+00 2 > > > but this expression doesn't make any sense because solve(V) doesn't exist. > > What I want is that R responses that mp or 4*mp is not diagonalizable and solve(V) doesn't exist. > > Arnau. > El 14/11/2011, a las 13:06, Martin Maechler escribió: > >> >>> 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 >>&...

...on R-2.2-1 and R-2.2-0 . ## Not seen in R-2.1.1 ! ## I haven't investiated whether it happens on Windows also. ### A few details on the matrix calculations : The eigenvalue decomposition is done on 4 * 4 matrices where the rows sum to 0. The matrices may be on the edge of not being complex diagonalizable. version _ platform i686-pc-linux-gnu arch i686 os linux-gnu system i686, linux-gnu status major 2 minor 2.1 year 2005 month 12 day 20 svn rev 36812 language R Thanks in advance of any help. Ole Christensen -- Ole F. Christensen BiRC - Bioinformatics R...

Hi, It is my understanding that the eigenvectors of a circulant matrix are given as follows: 1,omega,omega^2,....,omega^{p-1} where the matrix has dimension given by p x p and omega is one of p complex roots of unity. (See Bellman for an excellent discussion on this). The matrix created by the attached row and obtained using the following commands indicates no imaginary parts for the