We investigate the topological and metric structure of the set of idempotent operators and projections which have prescribed diagonal entries with respect to a fixed 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.
Giol, Julien; Kovalev, Leonid V.; Larson, David; Nguyen, Nga; and Tener, James E., "Projections and Idempotents with Fixed Diagonal and the Homotopy Problem for Unit Tight Frames" (2010). Mathematics Faculty Scholarship. Paper 50.
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