This is an upper triangular random matrix whose entries are drawn from the normal distribution with mean 0 and variance 1/N.
Unlike a matrix whose entries are all random, taking non-zero entries only in the upper (or lower) triangle produces a matrix with a high degree of non-normality [1,2].
[1]: J. M. Varah, "On the separation of two matrices", SIAM J. Numer. Anal. 16, pp. 216-222, 1979.
[2]: L. N. Trefethen, "Psuedospectra of matrices", in "Numerical Analysis 1991" (Dundee 1991), Longman Sci. Tech., Harlow, 1992, 234-266.
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