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In this paper nondegenerate multidimensional matrices of boundary format in V ⊗ ... ⊗ V are investigated by their link with Steiner vector bundles on product of projective spaces. For any nondegenerate matrix A the stabilizer for the SL(V) x ... x SL(V)-action, Stab(A), is completely described. In particular we prove that there exists an explicit action of SL(2) on V ⊗ ... ⊗ V such that Stab(A) ⊆ SL(2) and the equality holds if and only if A belongs to a unique SL(V) x ... x SL(V)-orbit containing...

We study general elements of moduli spaces ${\mathfrak{M}}_{{\mathbb{P}}^2}\left(2,c_1,c_2\right)$ of rank-2 stable holomorphic vector bundles on ${\mathbb{P}}^2$ and their minimal free resolutions. Incidentally, a quite easy proof of the irreducibility of ${\mathfrak{M}}_{{\mathbb{P}}^2}\left(2,c_1,c_2\right)$ is shown.