We show that the set of $m \times m$ complex skew-symmetric matrixpolynomials of odd grade $d$, i.e., of degree at most $d$, and (normal) rank atmost $2r$ is the closure of the single set of matrix polynomials with thecertain, explicitly described, complete eigenstructure. This completeeigenstructure corresponds to the most generic $m \times m$ complexskew-symmetric matrix polynomials of odd grade $d$ and rank at most $2r$. Inparticular, this result includes the case of skew-symmetric matrix pencils($d=1$).
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机译：我们证明，奇数级$ d $（即度最大为$ d $，且（正常）秩为$ 2r $）的$ m \ times m $复杂斜对称矩阵多项式的集合是单个集合的闭包具有明确描述的某些矩阵多项式的本征结构。这个完整的本征结构对应于奇数级$ d $且最高$ 2r $的最通用的$ m \乘m $复杂偏对称矩阵多项式。特别是，此结果包括倾斜对称矩阵铅笔（$ d = 1 $）的情况。
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