Anderson, W. N. jun.; Morley, T. D.; Trapp, G. E. Positive solutions to \(X=A-BX^{-1}B^*\). (English) Zbl 0702.15009 Linear Algebra Appl. 134, 53-62 (1990). The authors study the positive (semidefinite) solutions to the matrix equation \(X=A-BX^{-1}B^*\) under the assumption that \(A\geq 0\). It is shown that positive solutions exist if and only if a certain block tridiagonal operator is positive, in which case the solution is given by the generalized Schur complement of that operator. The Schur complement is considered to act on a proper subspace of a finite or infinite dimensional Hilbert space with inner product. Reviewer: M.de la Sen Cited in 78 Documents MSC: 15A24 Matrix equations and identities 15B48 Positive matrices and their generalizations; cones of matrices Keywords:bounded operators; matrix equation; positive solutions; Schur complement; Hilbert space; inner product × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Anderson, W. 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