[R] Question about converting from square roots to decimals and back

From: Robert Barber <robert.barber_at_comcast.net>
Date: Sat 20 Jan 2007 - 19:00:18 GMT


Hi,

I apologize if there is a simple answer to this question that I've missed. I did search the mailing list but I might not have used the right keywords. Why does sum(A3^2) give the result of 1, but sum(A3^2)==1 give the result of FALSE?

> A3<-matrix(nrow=3,c(1/(2^.5),1/(2^.5),0))
> A3

          [,1]

[1,] 0.7071068
[2,] 0.7071068
[3,] 0.0000000

> sum(A3^2)

[1] 1
> sum(A3^2)^.5

[1] 1
> sum(A3^2)==1 # here's the part I don't understand
[1] FALSE
> sum(A3^2)^.5==1 # here's the part I don't understand
[1] FALSE I realize that it has something to do with the conversion of the square roots into decimals. But shouldn't it then give me some number other than 1 as the result for sum(A3^2)? Are there other ways to do this than what I've tried? I'm trying to confirm that A3 is a unit vector.

Thank you for your help.

Bob B.



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