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We consider the covariance matrix for dichotomous Guttman items under a set of uniformity conditions, and obtain closed-form expressions for the eigenvalues and eigenvectors of the matrix. In particular, we describe the eigenvalues and eigenvectors of the matrix in terms of trigonometric functions of the number of items. Our results parallel those of Zwick… (More)

Partial orders can be represented by subsets of a given set ordered by inclusion. Special kinds of such set representations are investigated because they facilitate the exploration of properties of knowledge spaces. A new type of order relation is deÿned which is closely related to interval orders. These orders and the interval orders are investigated with… (More)

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