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How do I create a symmetric random matrix?

I want to create a random matrix that needs to be symmetrical.

I've tried this:

matrix(sample(0:1, 25, TRUE), 5, 5)

but it is not necessarily symmetrical.

How can i do this?

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3 answers


Try this from package Matrix 



library(Matrix)
x<-Matrix(rnorm(9),3)
x
3 x 3 Matrix of class "dgeMatrix"
           [,1]       [,2]       [,3]
[1,] -0.9873338  0.8965887 -0.6041742
[2,] -0.3729662 -0.5882091 -0.2383262
[3,]  2.1263985 -0.3550972  0.1067264

X<-forceSymmetric(x)
X
3 x 3 Matrix of class "dsyMatrix"
           [,1]       [,2]       [,3]
[1,] -0.9873338  0.8965887 -0.6041742
[2,]  0.8965887 -0.5882091 -0.2383262
[3,] -0.6041742 -0.2383262  0.1067264
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Another interesting possibility is based on the following mathematical fact: if A is some matrix, then A, multiplied by its transposition, is always symmetric.



> A <- matrix(runif(25), 5, 5)
> A %*% t(A)
         [,1]      [,2]      [,3]      [,4]      [,5]
[1,] 1.727769 1.0337816 1.2195505 1.4661507 1.1041355
[2,] 1.033782 1.0037048 0.7368944 0.9073632 0.7643080
[3,] 1.219551 0.7368944 1.8383986 1.3309980 0.9867812
[4,] 1.466151 0.9073632 1.3309980 1.3845322 1.0034140
[5,] 1.104135 0.7643080 0.9867812 1.0034140 0.9376534
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If you don't want to use the package:

n=3
x <- matrix(rnorm(n*n), n) 
ind <- lower.tri(x) 
x[ind] <- t(x)[ind] 
x
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