Nikiforov [11] introduced the concept of the \(A_{\alpha }\) -matrix as a convex linear combination of a graph’s adjacency matrix and its diagonal matrix of vertex degrees. In this paper, we introduce a new variant of the \(A_{\alpha }\) -matrix, which is a linear combination of the Hermitian adjacency matrix of the second kind, \(H^{\omega }\) , and the degree diagonal matrix D. We study the spectral properties of this matrix and obtain several bounds on its largest and smallest eigenvalues. In addition, we derive bounds for the spectral radius, spread, and trace norm (energy), yielding new spectral estimates for mixed graphs.
