In reply to arne.

I used the Kronecker product extensively in my MktEx macro, which among other things creates orthogonal array experimental designs. A large part of the macro is written in IML. If H is a 2x2 Hadamard matrix, {1 1, 1 -1}, then H provides the coding for a t-test (mean or intercept and one effect). H @ H is a 4x4 orthogonal array for three two-level factors. H @ H provides the coding for a two-way ANOVA. H @ H @ H is an 8x8 orthogonal array for seven two-level factors. ... and so on for larger products of H times itself. Kronecker products enable you to make larger arrays from smaller arrays. I also used it to concatenate vectors to themselves. Seeing this post brings back some fond memories.