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This monograph brings jointly my paintings in mathematical statistics as i've got seen it throughout the lens of Jordan algebras. 3 technical domain names are to be obvious: functions to random quadratic kinds (sums of squares), the research of algebraic simplifications of maxi mum chance estimation of patterned covariance matrices, and a extra vast open mathematical exploration of the algebraic area from which i've got drawn the consequences utilized in the statistical difficulties simply pointed out.
The first target of those lectures is to introduce a newbie to the finite dimensional representations of Lie teams and Lie algebras. considering this target is shared via various different books, we should always clarify during this Preface how our procedure differs, even though the capability reader can most likely see this greater through a short flick through the booklet.
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