We give a constructive proof of Carpenter's Theorem due to Kadison.
Unlike the original proof our approach also yields the
real case of this theorem.
diagonals of projections, the Schur-Horn theorem, the Pythagorean theorem, the Carpenter theorem, spectral theory
42C15 - General harmonic expansions, frames
47B15 - Hermitian and normal operators (spectral measures, functional calculus, etc.)
46C05 - Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)