Completions of positive semidefinite operator matrices
Mihály Bakonyi, Hugo J. Woerdeman · Princeton University Press eBooks · 2011
This chapter deals with positive definite and semidefinite completions of partial operator matrices. It considers the banded case in Section 2.1, the chordal case in Section 2.2, the Toeplitz case in Section 2.3, and the generalized banded case and the operator-valued positive semidefinite chordal case in Section 2.6. Section 2.4 introduces the Schur complement and uses it to derive an operator-valued Fejér–Riesz factorization. Section 2.5 is devoted to describing the structure of positive semidefinite operator matrices. Section 2.7 studies the Hamburger problem based on positive semidefinite completions of Hankel matrices. Finally, Section 2.8 indicates the connection with linear prediction. Exercises and notes are provided at the end of the chapter.