Message-ID: <i3mq00la7a1iobitevsdtq095n8gstbtgu@4ax.com>
Date: 2004-01-20T16:37:14Z
From: Duncan Murdoch
Subject: matrix exponential: M^0
In-Reply-To: <1074616806.2958.46.camel@monkey>
On 20 Jan 2004 16:40:07 +0000, Federico Calboli <f.calboli at ucl.ac.uk>
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:
R doesn't have a power operator that knows it's working on a matrix.
M^x raises each entry of M to the power x, it doesn't raise the matrix
to that power. E.g.
> x
[,1] [,2]
[1,] 2 2
[2,] 2 2
> x^2
[,1] [,2]
[1,] 4 4
[2,] 4 4
> x %*% x
[,1] [,2]
[1,] 8 8
[2,] 8 8
It's a little funny that 0^0 gives 1, but that's a reasonable
convention, often useful in likelihood calculations.
Duncan Murdoch