超廣義k次投影的線(xiàn)性組合群可逆和可逆性

2018-05-14 08:55付石琴劉曉冀

成都工業(yè)學(xué)院學(xué)報(bào) 2018年3期

付石琴　劉曉冀

參考文獻(xiàn)：

[1]BAKSALARY O M. Revisitation of generalized and hypergeneralized projectors[M]//Statistical Inference， Econometric Analysis and Matrix Algebra. Physica-Verlag HD， 2009：317-324.

[2]BENITEZ J， THOME N. Characterizations and linear combinations of k-generalized projectors [J]. Linear Algebra & Its Applications， 2005， 410（2）：150-159.

[3]鄧春源，李啟慧，杜鴻科. Generalized n-idempotents and Hyper-generalized n-idempotents[J]. Communications in Mathematical Research， 2006， 22（4）：387-394.

[4] BAKSALARY J， BAKSALARY O M， LIU X. Further properties of generalized and hypergeneralized projectors[J]. Linear Algebra & Its Applications， 2004， 389（1）：295-303.

[5] BAKSALARY J K， BAKSALARY O M， LIU X， et al. Further results on generalized and hypergeneralized projectors[J]. Linear Algebra & Its Applications， 2008， 429（5-6）：1038-1050.

[6] ZENG Y D， LIN L F， MATHEMATICS D O. Nonsingularity of linear combinations of idempotent matrices[J]. Linear Algebra & Its Applications， 2013， 388（1）：25-29.

[7]LIU X， WU S， BENITEZ J. On nonsingularity of combinations of two group invertible matrices and two tripotent matrices[J]. Linear & Multilinear Algebra， 2011， 59（12）：1409-1417.

[8]TOSIC M. Characterizations and the Moore-Penrose inverse of hypergeneralized k-projectors[J]. Bulletin of the Korean Mathematical Society， 2014， 51（2）：438-441.

[9] M， D S， DENG C. The Moore-Penrose inverse of a linear combination of commuting generalized and hypergeneralized projectors[J]. Electronic Journal of Linear Algebra Ela， 2011， 22（1）：1129-1137.

[10] LIU X， ZHANG M， JULIO B. Expressions of the group inverse of the linear combinations of k-ldempotent matrices and the Moore-Penrose generalized lnverse of the linear combinations of the hypergeneralized ldempotent matrices[J]. Chinese Annals of Mathematics， 2014，35（4）：463-478.

[11] ZUO K. Nonsingularity of the difference and the sum of two idempotent matrices[J]. Linear Algebra & Its Applications， 2010， 433（2）：476-482.

[12]LI H Y，ZUO K Z. The study of idempotence， reversibility， the group inverse， D-inverse， M-P inverse of combination for two special operator[J]. Applied Mathematics， 2014：19-25.

[13]MEYER C. Matrix analysis and applied linear algebra[M]. Society for Industrial and Applied Mathematics， 2000.

[14] J. Moore-Penrose inverses and commuting elements of C*-algebras[J]. Journal of Mathematical Analysis & Applications， 2008， 345（2）：766-770.