A Matrix Inequality for the Inversions of the Restrictions of a Positive Definite Hermitian Matrix - Advances in Linear Algebra & Matrix Theory

ALAMT > Vol.3 No.4, December 2013

Advances in Linear Algebra & Matrix Theory

Volume 3, Issue 4 (December 2013)

ISSN Print: 2165-333X ISSN Online: 2165-3348

Google-based Impact Factor: 0.14 Citations

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

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DOI: 10.4236/alamt.2013.34011 4,357 Downloads 9,388 Views Citations

Author(s)

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

Affiliation(s)

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.

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

Share and Cite:

Mai, W. , Yan, M. , Qian, T. , Riva, M. and Saitoh, S. (2013) A Matrix Inequality for the Inversions of the Restrictions of a Positive Definite Hermitian Matrix. Advances in Linear Algebra & Matrix Theory, 3, 55-58. doi: 10.4236/alamt.2013.34011.

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