Abstract
An essential subproblem in the study of invariants of homogeneous matrix pencils sF − ŝG under bilinear strict equivalence is the study of complex projective equivalence (PE), ℰp, defined on the set ℂk of complex homogeneous binary polynomials of fixed homogeneous degree k. For an ƒ(s, ŝ)∈ℂk, the study of invariants of the PE class ℰp(ƒ) is reduced to a study of invariants of matrices of the set ℂm × 2∗ (m×2 matrices with all 2×2 minors nonzero) under extended Hermite equivalence (EHE), ℰeH. For the equivalence class ℰeH(T), T ∈ℂm×2∗, it is shown that if m = 1,2,3 then ℰeH = ℂm×2∗. For the case m ⩾ 4, ℰeH(T) is characterized by a complete set of invariants, the set of Plücker vectors ℘(T) of T. These results lead to the definition of new sets of invariants for the class ℰp(f), which are the Plücker vectors ℘(f) and the list of degrees, ℐ(f), of the elementary divisors of f(s, ŝ).
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