[R] matrix exponential: M^0

[Stephane DRAY]

Hello,
be careful D^0 is not the zeroeth power of a matrix. It is a term power 
:D[i,j]^0=1

To obtain the power of a matrix, you can use a decomposition such as svd:

X = U D V'
the n-th power of X is X = U D^n V'


svd1=svd(D)
Apower0=svd1$u%*%diag(svd1$d^0)%*%t(svd1$v)


At 11:40 20/01/2004, Federico Calboli wrote:
>Dear All,
>
>I would like to ask why the zeroeth power of a matrix gives me a matrix
>of ones rather than the identity matrix:
>
> > D<-rbind(c(0,0,0),c(0,0,0),c(0,0,0))
> > D<-as.matrix(D)
> > D
>      [,1] [,2] [,3]
>[1,]    0    0    0
>[2,]    0    0    0
>[3,]    0    0    0
>
> > D^0
>      [,1] [,2] [,3]
>[1,]    1    1    1
>[2,]    1    1    1
>[3,]    1    1    1
>
>I would have expected the identity matrix here.
>
>I find the same result with every other square matrix I used.
>BTW, I am using R 1.8.1 on Linux Mandrake 9.1
>
>Cheers,
>
>Federico Calboli
>--
>
>
>
>=================================
>
>Federico C. F. Calboli
>
>PLEASE NOTE NEW ADDRESS
>
>Dipartimento di Biologia
>Via Selmi 3
>40126 Bologna
>Italy
>
>tel (+39) 051 209 4187
>fax (+39) 051 251 208
>
>f.calboli at ucl.ac.uk
>
>______________________________________________
>R-help at stat.math.ethz.ch mailing list
>https://www.stat.math.ethz.ch/mailman/listinfo/r-help
>PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html

Stéphane DRAY
-------------------------------------------------------------------------------------------------- 

Département des Sciences Biologiques
Université de Montréal, C.P. 6128, succursale centre-ville
Montréal, Québec H3C 3J7, Canada

Tel : 514 343 6111 poste 1233
E-mail : stephane.dray at umontreal.ca
-------------------------------------------------------------------------------------------------- 

Web                                          http://www.steph280.freesurf.fr/