yes, the matrix is symmetric.
But when I apply normalize upon rows, I expect to get the following result:
> apply( a, 1, normalize )
[,1] [,2] [,3] [,4] [,5]
[1,] 0.00 0.25 0.50 0.75 1.00
[2,] 0.00 0.25 0.50 0.75 1.00
[3,] 0.00 0.25 0.50 0.75 1.00
[4,] 0.00 0.25 0.50 0.75 1.00
[5,] 0.00 0.25 0.50 0.75 1.00
Actually we can get asymmetric matrix like:
> a = c(1:5) %*% t(1:5)
> a
[,1] [,2] [,3] [,4] [,5]
[1,] 5 4 3 2 1
[2,] 10 8 6 4 2
[3,] 15 12 9 6 3
[4,] 20 16 12 8 4
[5,] 25 20 15 10 5
> apply(a, 2, normalize)
[,1] [,2] [,3] [,4] [,5]
[1,] 0.00 0.00 0.00 0.00 0.00
[2,] 0.25 0.25 0.25 0.25 0.25
[3,] 0.50 0.50 0.50 0.50 0.50
[4,] 0.75 0.75 0.75 0.75 0.75
[5,] 1.00 1.00 1.00 1.00 1.00
>
> apply(a, 1, normalize)
[,1] [,2] [,3] [,4] [,5]
[1,] 1.00 1.00 1.00 1.00 1.00
[2,] 0.75 0.75 0.75 0.75 0.75
[3,] 0.50 0.50 0.50 0.50 0.50
[4,] 0.25 0.25 0.25 0.25 0.25
[5,] 0.00 0.00 0.00 0.00 0.00
the latter result is very strange.
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