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It is easy to generate a matrix with maximal rank. As a random matrix has a very high probability of being of maximal rank, especially when the range of the coefficients is not too small, one can generate a matrix of given dimension, test the rank, then go back to generate another if the rank is small.

Or, if loop is not provided in the syntax, two triangular matrices of proper dimensions with non-zero elements on the diagonal can be generated first, then a multiplication of the two matrices with give a matrix of maximal rank.

In order to generate a random matrix of dimension m&times;n and of rank r such that r&lt;min(m,n), one can first generate two random matrices A,B of maximal ranks, of dimensions m&times;r and r&times;n respectively. Then the product AB will be a matrix meeting the requirements.