Spectral decomposition

2 messages · Marcos Sanches, Peter Dalgaard

Mon, Mar 11, 2002 6:22 AM #

Hello all,

    I have the square symetric matrix A:
2 1 1
1 2 1
1 1 2
  My first question is what is the easiest way to enter this matriz in R?
Second, matrix A has an eigenvalue with multiplicity 2, in this case, how
could I find the two related ortogonal eigenvectors given below by R,
without the help of R, I mean, I want to know how R calculate this
eigenvectors related to the same eigenvalue.

$values
[1] 4 1 1

$vectors
          [,1]       [,2]        [,3]
[1,] 0.5773503  0.8161298  0.02447130
[2,] 0.5773503 -0.3868721 -0.71902477
[3,] 0.5773503 -0.4292577  0.69455348

Thanks very much,

Marcos


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Peter Dalgaard

Mon, Mar 11, 2002 6:30 AM #

"Marcos Sanches" <marcos_sanches at gallup.com> writes:

Depends on the generality you need in the solution. 

m <- 1+diag(3) is probably the shortest.

O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907
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