2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69830The well known formula of B. Fuglede expresses the mean value of the Radon k-plane transform on $R^n$ as a Riesz potential. We extend this formula to the space of $n \times m$ real matrices and show that the corresponding matrix k-plane transform $f \to \hat f$ is injective if and only if $n-k \ge m$. Different inversion formulas for this transform are obtained. We assume that $f \in L^p$ or $f$ is a continuous function satisfying certain "minimal" conditions at infinity.AMS LaTeX, 20 pagesFunctional AnalysisPrimary 44A12; Secondary 47G10text