[R] matrix of eigenvalues
Christian Jost
jost at cict.fr
Tue Oct 19 10:18:27 CEST 2004
I thought that the function
eigen(A)
will return a matrix with eigenvectors that are independent of each
other (thus forming a base and the matrix being invertible). This
seems not to be the case in the following example
A=matrix(c(1,2,0,1),nrow=2,byrow=T)
eigen(A) ->ev
solve(ev$vectors)
note that I try to get the upper triangular form with eigenvalues on
the diagonal and (possibly) 1 just atop the eigenvalues to be used to
solve a linear differential equation
x' = Ax, x(0)=x0
x(t) = P exp(D t) P^-1 x0
where D is this upper triangular form and P is the "passage matrix"
(not sure about the correct english name) given by a base of
eigenvectors. So the test would be
solve(ev$vectors) %*% A %*% ev$vectors - D
should be 0
Thanks for any help, Christian.
ps: please copy reply also to my address, my subscription to the
R-help list seems to have delays
--
***********************************************************
http://cognition.ups-tlse.fr/vas-y.php?id=chj jost at cict.fr
Christian Jost (PhD, MdC)
Centre de Recherches sur la Cognition Animale
Universite Paul Sabatier, Bat IV R3
118 route de Narbonne
31062 Toulouse cedex 4, France
Tel: +33 5 61 55 64 37 Fax: +33 5 61 55 61 54
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