论文标题
具有基质重量的树木的平方距离矩阵
Squared distance matrices of trees with matrix weights
论文作者
论文摘要
让$ t $为$ n $顶点的一棵树，其边缘权重是订单$ s $的确定矩阵。 $δ$表示的$ t $的平方距离矩阵是$ ns \ times ns $ block矩阵，带有$δ_{ij} = d（i，j）^2 $，其中$ d（i，j）$是唯一$（i，j）$ path的边缘权重的总和。在本文中，我们获得了$δ$的决定因素的公式，并在某些条件下找到$δ^{ - 1} $。
Let $T$ be a tree on $n$ vertices whose edge weights are positive definite matrices of order $s$. The squared distance matrix of $T$, denoted by $Δ$, is the $ns \times ns$ block matrix with $Δ_{ij}=d(i,j)^2$, where $d(i,j)$ is the sum of the weights of the edges in the unique $(i,j)$-path. In this article, we obtain a formula for the determinant of $Δ$ and find $Δ^{-1}$ under some conditions.
