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

[Robert Barber]

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.