We show that the Christensen-Sinclair factorization theorem, when the underlying Hilbert spaces are finite dimensional, is an instance of strong duality of semidefinite programming. This gives an elementary proof of the result and also provides an efficient algorithm to compute the Christensen-Sinclair factorization.

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doi.org/10.1016/j.laa.2025.03.007
Linear Algebra and its Applications
Networks , Marie Skłodowska-Curie

Escudero Gutiérrez, F. (2025). Christensen-Sinclair factorization via semidefinite programming. Linear Algebra and its Applications, 714, 28–44. doi:10.1016/j.laa.2025.03.007