NDLI: The Generalized Inverse Inequalities for Symmetric Nonnegative Definite Matrices

Content Provider	IEEE Xplore Digital Library
Author	Shiqing Wang Mingqing Dai
Copyright Year	2010
Abstract	Let be symmetric positive definite matrix, symmetric nonnegative definite matrix. If the difference of and is positive definite, then the difference of and is also positive definite. If, are all symmetric nonnegative definite matrices, Milliken and Akdeniz (1977) proved that they also have this relationship if only the ranks of the two matrices are same. That is the difference of and is symmetric nonnegative definite, where is Penrose-Moore inverse matrix of . Wang (2010) improved this inequality and extended by his result Belmega’s (2009) a theorem. In this paper, we give some inequalities of the sum and the product for symmetric nonnegative definite matrix. They all extend Milliken and Akdeniz’s (1977) and Wang’s (2010) results.
Starting Page	547
Ending Page	550
File Size	307930
Page Count	4
File Format	PDF
ISBN	9781424484324
DOI	10.1109/AICI.2010.353
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-10-23
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Presses Information science Symmetric matrices Symmetric nonnegative definite matrix Generalized inverse matrix Column space Matrices Symmetric positive definite matrix Linear matrix inequalities Equations Inequality Penrose-Moore inverse matrix
Content Type	Text
Resource Type	Article

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The Generalized Inverse Inequalities for Symmetric Nonnegative Definite Matrices