[R] matrix of eigenvalues

[Christian Jost]

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