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We investigate the topological and metric structure of the set of idempotent operators and projections which have prescribed diagonal entries with respect to a Þxed orthonormal basis of a Hilbert space. As an application, we settle some cases of conjectures of Larson, Dykema, and Strawn on the connectedness of the set of unit-norm tight frames.

Projections and idempotents with fixed diagonal and the homotopy problem for unit tight frames