A Matrix Inequality for the Inversions of the Restrictions of a Positive Definite Hermitian Matrix

Weixiong Mai, Mo Yan, Tao Qian, Matteo Dalla Riva, Saburou Saitoh

Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, Aveiro, Portugal.
Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau, China.

DOI: 10.4236/alamt.2013.34011                

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.

Keywords

Reproducing Kernel; Positive Definite Hermitian Matrix; Quadratic Inequality; Inversion of Positive Definite Hermitian Matrix; Restriction of Positive Definite Hermitian Matrix; Schur Complement; Block Matrix

Conflicts of Interest

The authors declare no conflicts of interest.

References

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