Identified are certain special periodic diagonal matrices that have a predictable number of paired eigenvalues. Since certain symmetric Toeplitz matrices are special cases, those that have several multiple 5 eigenvalues are also investigated further. This work generalizes earlier work on response matrices from circularly symmetric models.
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This article is about polynomial maps with a certain symmetry and/or antisymmetry in their Jacobians, and whether the Jacobian Conjecture is satisfied for such maps, or whether it is sufficient to prove the Jacobian Conjecture for such maps. For instance, we show that it suffices to prove the Jacobian conjecture for polynomial maps x + H over ℂ such that satisfies all symmetries of the square, where H is homogeneous of arbitrary degree d ≥ 3.
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