Even grade generic skew-symmetric matrix polynomials with bounded rank (Q6618716)

The authors prove that the closure of the only set of matrix polynomials with a specific, fully defined eigenstructure is the set of \(m\) square complex skew-symmetric matrix polynomials of even grade \(d\) and (normal) rank at most \(2r\). The most general \(m \times m\) complex skew-symmetric matrix polynomials of even grade \(d\) and rank at most \(2r\) are represented by this full eigenstructure. For the situation of skew-symmetric matrix polynomials of odd grade, the related problem raised by the second and the third author in [Linear Algebra Appl. 536, 1--18 (2018; Zbl 1373.15017)] is solved.