Let $G=(V(G),E(G))$ be a simple graph with vertex set $V(G)={v_{1},v_{2},cdots, v_{n}}$ and edge set $E(G)$. The $p$-Sombor matrix $mathcal{S}_{p}(G)$ of $G$ is defined as the $(i,j)$ entry is $((d_{i})^{p}+(d_{j})^{p})^{frac{1}{p}}$ if $v_{i}sim v_{j}$, and 0 otherwise, where $d_{i}$ denotes the degree of vertex $v_{i}$ in $G$. In this paper, we study the relationship between $p$-Sombor index $SO_{p}(G)$ and $p$-Sombor matrix $S_{p}(G)$ by the $k$-th spectral moment $N_{k}$ and the spectral radius of $S_{p}(G)$. Then we obtain some bounds of $p$-Sombor Laplacian spectrum, $p$-Sombor spectral radius, $p$-Sombor spectral spread, $p$-Sombor energy and $p$-Sombor Estrada index. We also investigate the Nordhaus-Gaddum-type results for $p$-Sombor spectral radius and energy. At last, we give the regression model for boiling point and some other invariants.
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