In this paper, we explore the class of nonnegative matrices by finding an exact identity for the Schatten p-numerical radii of these matrices. More precisely, we prove that if A is an \(n\times n\) matrix with nonnegative entries, and if \(p\ge 2\) is an even integer, then \(\begin{aligned} \omega _p(A)=\left\| \Re \left( A\right) \right\| _p, \end{aligned}\) where \(\omega _p(\cdot )\) and \( \Vert \cdot \Vert _p\) are the Schatten \(p-\) numerical radius and norm, respectively, while \(\Re (\cdot )\) is the real part. This result extends the same conclusion that has been known for the (usual) numerical radius. A wide spectrum of applications will be presented, where monotonicity and power-type inequalities will be shown, in addition to an exact identity. Further investigation of nonnegative block matrices will also lead to numerous new bounds that extend many known results in the literature.
