论文标题
Loewy-Radwan猜想的解决方案
The solution of the Loewy-Radwan conjecture
论文作者
论文摘要
Gerstenhaber的开创性结果给出了Nilpotent矩阵线性空间的最大维度。它还显示了达到最大维度的该空间的结构。已经研究了该导致该矩阵的线性空间的扩展，并研究了具有界数特征值的矩阵。在本文中，我们回答了Loewy和Radwan提出的最普遍的问题，即通过解决阳性的猜想来回答。我们给出$ n \ times n $矩阵的最大线性空间的尺寸，不超过$ k <n $ eigenvalues。我们还展示了达到该维度的空间的结构。
A seminal result of Gerstenhaber gives the maximal dimension of a linear space of nilpotent matrices. It also exhibits the structure of this space where the maximal dimension is attained. Extensions of this result in the direction of linear spaces of matrices with a bounded number of eigenvalues have been studied. In this paper, we answer perhaps the most general problem of the kind as proposed by Loewy and Radwan by solving their conjecture in the positive. We give the dimension of a maximal linear space of $n\times n$ matrices with no more than $k<n$ eigenvalues. We also exhibit the structure of the space where this dimension is attained.
