Matlab - generate random nonsingular triangular matrix

Question

How can I generate a random triangular matrix? (upper and lower)

Usually I use rand(n) but if I try tril(rand(n)) it will be singular and I don't want that.

Answer 1

your answer is correct:

 A=tril(rand(n))

you can check that this matrix is not singular using

 rcond(A)>eps

or

 min(svd(A))>eps

and verifying that the smallest singular value is larger than eps, or any other numerical tolerance that is relevant to your needs. (the code will return 1 or 0). For n>50 you'll start to approach singular matrices.

Here's a small analysis of how the matrix approaches singularity with it's size...