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In quantum physics, scientists use mathematical tools to identify hidden symmetries in complex materials known as topological phases. Previous methods relied on simple numbers, or scalars, to measure these symmetries, which often accidentally erased crucial details about how particles interact. The current research introduces a new, matrix-based measurement tool. By keeping the full mathematical matrix rather than compressing it into a single number, physicists can now detect subtle, previously invisible interactions and structural details in non-Abelian quantum systems.