matrix exponential: M^0
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
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