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Positive solutions to $X=A-BX\sp{-1}B\sp*$. (English) Zbl 0702.15009
The authors study the positive (semidefinite) solutions to the matrix equation $X=A-BX\sp{-1}B\sp*$ under the assumption that $A\ge 0$. 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

15A24Matrix equations and identities
15B48Positive matrices and their generalizations; cones of matrices
Full Text: DOI
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