spectrum and energy of the sombor matrix

Introduction/purpose: the sombor matrix is a vertex-degree-based matrix associated with the sombor index. the paper is concerned with the spectral properties of the sombor matrix. results: equalities and inequalities for the eigenvalues of the sombor matrix are obtained, from which two fundamental bounds for the sombor energy (= energy of the sombor matrix) are established. these bounds depend on the sombor index and on the forgotten topological index. conclusion: the results of the paper contribute to the spectral theory of the sombor matrix, as well as to the general spectral theory of matrices associated with vertex-degree-based graph invariants.