2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58361The determinant for complex matrices cannot be extended to quaternionic matrices. Instead, the Study determinant and the closely related $q$-determinant are widely used. We show that the Study determinant can be characterized as the unique functional which extends the {\em absolute value} of the complex determinant and discuss its spectral and linear algebraic aspects.12 pages, AMS-TeXMathematical Physicstext