An Analog of the Adjugate Matrix for the Outer Inverse ð ´ ( 2 ) 𠑇, 𠑆

Xiaoji Liu, Guangyan Zhu, Guangping Zhou and Yaoming Yu

Mathematical Problems in Engineering, 2012, vol. 2012, 1-14

Abstract:

We investigate the determinantal representation by exploiting the limiting expression for the generalized inverse ð ´ ( 2 ) 𠑇 , 𠑆 . We show the equivalent relationship between the existence and limiting expression of ð ´ ( 2 ) 𠑇 , 𠑆 and some limiting processes of matrices and deduce the new determinantal representations of ð ´ ( 2 ) 𠑇 , 𠑆 , 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 î ‚ 𠑆 ð ´ ð ‘‹ ð µ = ð · , â„› ( ð ‘‹ ) ⊂ 𠑇 , ð ’© ( ð ‘‹ ) ⊃ .

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:591256

DOI: 10.1155/2012/591256

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