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Matrix mathematics provides a powerful tool set for addressing statistical problems, in particular, the theory of matrix ranks and inertias has been developed as effective methodology of simplifying various complicated matrix expressions, and establishing equalities and inequalities occurred in statistical analysis. This paper describes how to establish exact formulas for calculating ranks and inertias...
Let x, y be two distinct real numbers. An {x, y}-matrix is a matrix whose entries are either x or y. We determine the possible numbers of x’s in an {x, y}-matrix with a given rank. Our proof is constructive.
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