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I want to generate a random matrix which should be symmetric.
I have tried this:
matrix(sample(0:1, 25, TRUE), 5, 5)
but it is not necessarily symmetric.
How can I do that?
436
A matrix is symmetric if and only if it is equal to its transpose. All entries above the main diagonal of a symmetric matrix are reflected into equal entries below the diagonal. A matrix is skew-symmetric if and only if it is the opposite of its transpose. All main diagonal entries of a skew-symmetric matrix are zero.
Another quite interesting opportunity is based on the following mathematical fact: if A is some matrix, then A multiplied by its transpose 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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