论文标题
格拉斯曼尼亚人的凸面和对称性过度的组合
Convex Hulls of Grassmannians and Combinatorics of Symmetric Hypermatrices
论文作者
论文摘要
众所周知，可以用$ k $二维子空间的复杂的司羊grass段质量级别的投影矩阵来识别$ k $。在经典上，该集合的凸壳是赫米尔式矩阵的集合，其特征值在$ 0 $至$ 1 $之间，总结到$ k $。我们给出了这个事实的新证明。我们还通过类似的论点为特定组合类别的过度标准提供了一个存在定理。可以将这种存在定理重写为具有给定的加权度序列的均匀加权超图的存在定理。
It is known that the complex Grassmannian of $k$-dimensional subspaces can be identified with the set of projection matrices of rank $k$. It is also classically known that the convex hull of this set is the set of Hermitian matrices with eigenvalues between $0$ and $1$ and summing to $k$. We give a new proof of this fact. We also give an existence theorem for a certain combinatorial class of hypermatrices by a similar argument. This existence theorem can be rewritten into an existence theorem for a uniform weighted hypergraph with given weighted degree sequence.
