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I want to create a matrix where each entry itself is a random matrix. What would be a good way to represent this?

It is not necessary but some hints on how to implement your proposed solution in Python would be useful.

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What you are looking for is just a higher dimensional array.

Let's say you want a 5x5 array where each element is a 2x2 array with random number. You can easily represent that as a 5x5x2x2 array.

If you are happy about using numpy

A = numpy.random.rand(5,5,2,2)

Will create a 5x5x2x2 array.

You can use the first two indexes to access your 2D random arrays.

print A[1,1]

Results in:

[[ 0.68527006  0.37304491]
 [ 0.23281899  0.46951261]]
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