Jeffries, Clarkvan den Driessche, P.2009-08-282009-08-2819862009-08-28http://hdl.handle.net/1828/1674In this note we consider real matrices whose associated undirected graphs are trees. Our goal is to establish finitely computable tests for the magnitudes of multiplicities of eigenvalues of such matrices. Using our tests for certain system designs expressed as signed directed graphs, the controllability of associated linear dynamical systems can be guaranteed.entechnical reports (mathematics and statistics)Technical ReportDepartment of MathematicsDepartment of Mathematics and Statistics