论文标题
某些特殊矩阵的双节性分解和总阳性
Bidiagonal decompositions and total positivity of some special matrices
论文作者
论文摘要
矩阵$ s = [1+x_i y_j] _ {i，j = 1}^{n}，0 <x_1 <x_1 <\ cdots <x_n，\，0 <y_1 <\ cdots <y_n $，由于其在保留总体非维持势力方面的作用，因此最近变得非常重要。我们在基本bidiagonal矩阵方面对$ s $进行了明确的分解，该矩阵类似于内维尔分解。我们给出了$ s^{\ circ m} = [（1+x_iy_j）^m] $的bidiagonal分解。我们还探讨了另一类称为平均矩阵的矩阵的Hadamard权力的总积极性。
The matrix $S = [1+x_i y_j]_{i,j=1}^{n}, 0<x_1<\cdots<x_n,\, 0<y_1<\cdots<y_n$, has gained importance lately due to its role in powers preserving total nonnegativity. We give an explicit decomposition of $S$ in terms of elementary bidiagonal matrices, which is analogous to the Neville decomposition. We give a bidiagonal decomposition of $S^{\circ m}=[(1+x_iy_j)^m]$ for positive integers $1\leq m \leq n-1$. We also explore the total positivity of Hadamard powers of another important class of matrices called mean matrices.
