  Let $G$ be a simple undirected graph with vertex set $V(G)=\{v_1, v_2,
\ldots, v_n\}$ and edge set $E(G)$. The Sombor matrix $\mathcal{S}(G)$ of a
graph $G$ is defined so that its $(i,j)$-entry is equal to $\sqrt{d_i^2+d_j^2}$
if the vertices $v_i$ and $v_j$ are adjacent, and zero otherwise, where $d_i$
denotes the degree of vertex $v_i$ in $G$. In this paper, lower and upper
bounds on the spectral radius, energy and Estrada index of the Sombor matrix of
graphs are obtained, and the respective extremal graphs are characterized.
