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A Matrix Inequality for the Inversions of the Restrictions of a Positive Definite Hermitian Matrix
Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau, China
Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau, China
Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau, China
Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, Aveiro, Portugal
Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, Aveiro, Portugal
- 1 Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau, China
- 2 Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau, China
- 3 Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau, China
- 4 Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, Aveiro, Portugal
- 5 Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, Aveiro, Portugal
Advances in Linear Algebra & Matrix Theory·Volume 03 (2013)·Pages 55–58·Published 6 December 2013·DOI10.4236/alamt.2013.34011
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Abstract
We exploit the theory of reproducing kernels to deduce a matrix inequality for the inverse of the restriction of a positive definite Hermitian matrix.
KeywordsReproducing KernelPositive Definite Hermitian MatrixQuadratic InequalityInversion of Positive Definite Hermitian MatrixRestriction of Positive Definite Hermitian MatrixSchur ComplementBlock Matrix
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