论文标题
某些特殊矩阵的阳性特性
Positivity properties of some special matrices
论文作者
论文摘要
结果表明，对于正实数，$ 0<λ_{1} <\ dots<λ_{n} $，$ \ left [\ frac {1} {β（{λ_i}，{λ_Jj}} \ right] $，其中$β（\ cdot，\ cdot，\ cdot）$ cdot and becta和inffine beda and infina bebise n.对于$ \ left [\ frac {1} {β（{i}，{j}）} \ right] $，计算了cholesky的分解和连续的基本竞技表分解。令$ \ mathfrak w（n）$为$ n $ th bell号码。事实证明，$ \ left [\ mathfrak w（i+j）\ right] $是一个完全积极的矩阵，但仅限订购$ 4 $才能无限分区。还表明，对称的Stirling矩阵是完全积极的。
It is shown that for positive real numbers $ 0<λ_{1}<\dots<λ_{n}$, $\left[\frac{1}{β({λ_i}, {λ_j})}\right]$, where $ β(\cdot,\cdot)$ denotes the beta function, is infinitely divisible and totally positive. For $ \left[\frac{1}{β({i},{j})}\right]$, the Cholesky decomposition and successive elementary bidiagonal decomposition are computed. Let $\mathfrak w(n)$ be the $n$th Bell number. It is proved that $\left[\mathfrak w(i+j)\right]$ is a totally positive matrix but is infinitely divisible only upto order $4$. It is also shown that the symmetrized Stirling matrices are totally positive.
