How to create a m by n matrix in which each element be another p by q matrix?

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You cannot do so, as a regular 2-d matrix. (As Roger pointed out.)
You can do so easily enough however, using a 4-dimensional array.
A = rand(p,q,100,100);
A is a 4-d array. You can create the array in a variety of ways. I used random elements. But now
A(:,:,i,j)
is a pxq matrix, as you desire.
Roger Stafford
Roger Stafford am 27 Feb. 2015
You cannot do that with matrices. Each of their elements must be a single scalar quantity. However, you can do such things using cell arrays.

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