An Analog of the Adjugate Matrix for the Outer Inverse AT, S(2). (19th February 2012)

• Record Type: Journal Article
• Authors: Liu, Xiaoji; Zhu, Guangyan; Zhou, Guangping; Yu, Yaoming
• Other Names: Chen Kui Fu Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2012(2012)
• Publication Date: 2012-02-19
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2012/591256
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : We investigate the determinantal representation by exploiting the limiting expression for the generalized inverse A T, S ( 2 ) . We show the equivalent relationship between the existence and limiting expression of A T, S ( 2 ) and some limiting processes of matrices and deduce the new determinantal representations of A T, S ( 2 ), based on some analog of the classical adjoint matrix. Using the analog of the classical adjoint matrix, we present Cramer rules for the restricted matrix equation A X B = D, R ( X ) ⊂ T, N ( X ) ⊃ S ∼ .