[R] matrix power

[(Ted Harding)]

On 10-Aug-09 21:31:30, cindy Guo wrote:
> Hi, All,
> If I  have a symmetric matrix, how can I get the negative square root
> of the matrx, ie. X^(-1/2) ?
> 
> Thanks,
> 
> Cindy

  X <- matrix(c(2,1,1,2),nrow=2)
  X
#      [,1] [,2]
# [1,]    2    1
# [2,]    1    2

  E <- eigen(X)
  V <- E$values
  Q <- E$vectors
  Y <- Q%*%diag(1/sqrt(V))%*%t(Q)
  Y
#            [,1]       [,2]
# [1,]  0.7886751 -0.2113249
# [2,] -0.2113249  0.7886751

  solve(Y%*%Y)    ## i.e. find its inverse
#      [,1] [,2]
# [1,]    2    1
# [2,]    1    2

Hence (Y%*%Y)^(-1) = X, or Y = X^(-1/2)

Hopingb this helps,
Ted.

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E-Mail: (Ted Harding) <Ted.Harding at manchester.ac.uk>
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Date: 10-Aug-09                                       Time: 22:53:25
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