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Let $T$ be a tree on $n$ vertices whose edge weights are positive definitematrices of order $s$. The squared distance matrix of $T$, denoted by $\Delta$,is the $ns \times ns$ block matrix with $\Delta_{ij}=d(i,j)^2$, where $d(i,j)$is the sum of the weights of the edges in the unique $(i,j)$-path. In thisarticle, we obtain a formula for the determinant of $\Delta$ and find${\Delta}^{-1}$ under some conditions.

Squared distance matrices of trees with matrix weights