TY  - JOUR
T1  - Some Expressions for the Group Inverse of the Block Partitioned Matrices with an Invertible Subblock
TT  - Tersinir Bir Altbloğa Sahip Blok Parçalanmiş Matrislerin Grup İnversleri İçin Bazı İfadeler
AU  - Maden, Selahattin
PY  - 2018
DA  - June
JF  - Ordu Üniversitesi Bilim ve Teknoloji Dergisi
JO  - Ordu Üniv. Bil. Tek. Derg.
PB  - Ordu University
WT  - DergiPark
SN  - 2146-6440
SP  - 100
EP  - 113
VL  - 8
IS  - 1
LA  - en
AB  -  Let                               be a skew fieldand   be the set ofall   matrices over    The purpose ofthis paper is to give some necessary and sufficient conditions for theexistence and some expressions of the group inverse of the block matrix     (  is square) undersome conditions, where    be a squareblock matrix with an invertible subblock. 
KW  - Skew field
KW  - Block partititoned matrix
KW  - Group Inverse of a matrix
KW  - Invertible subblock
KW  - Drazin inverse
N2  -  bir kesircismi ve     de bukesir cismi üzerindeki   tipindekitüm matrislerin kümesi olsun. Bu çalışmadaki amaç,   tersinirbir alt bloğa sahip blok parçalanmış bir kare matris olmak üzere,     (  bir karematris) matrisinin grup inversinin mevcut olması için gerek ve yeter şartlarıvermek ve bazı koşullar altında blok parçalanmış matrislerin grup inversi içinifadeler elde etmektir
CR  - 1.	Ben-Israel A & Greville T N E (2003). Generalized Inverses: Theory and Applications, 2. ed., Wiley, New York.
CR  - 2.	Bu C, Zhao J & Zheng J (2008). Group inverse for a class 2x2 block matrices over skew fields, Appl. Math. Comput. 204: 45–49.
CR  - 3.	Bu C, Zhao J & Zheng J (2009). Some results on group inverses of the block matrix over skew fields, Eelectro. J.  Linear Algebra 18: 117-125.
CR  - 4.	Campbell S (1983). The Drazin inverse and systems of second order linear differential equations, Linear Multilinear Algebra 14: 195–198.
CR  - 5.	Campbell S L & Meyer C D (1991). Generalized Inverses of Linear Transformations, Pitman, London, Dover, New York.
CR  - 6.	Cao C (2001). Some results of group inverses for partitioned matrices over skew fields, J. Natural Sci. Heilongjiang Univ. 18 (3): 5–7.
CR  - 7.	Cao C & Tang X (2006). Representations of the group inverse of some 2x2 block matrices, Int. Math. Forum 31: 1511–1517.
CR  - 8.	Chen X & Hartwig R E (1996). The group inverse of a triangular matrix, Linear Algebra Appl. 237/238: 97–108.
CR  - 9.	Cvetkovic -Ilic D S (2008). A note on the representation for the Drazin inverse of 2x2 block matrices, Linear Algebra Appl. 429: 242–248.
CR  - 10.	González N C & Dopazo E (2005). Representations of the Drazin inverse of a class of block matrices, Linear Algebra Appl. 400: 253–269.
CR  - 11.	González N C, Dopazo E & Robles J (2006). Formulas for the Drazin inverse of special block matrices, Appl. Math. Comput. 174: 252–270.
CR  - 12.	Hartwig R E & Shoaf J M (1977). Group inverse and Drazin inverse of diagonal and triangular Toeplitz matrices, Aust. J. Math. 24: 10–34.
CR  - 13.	Hartwig R, Li X & Wei Y (2006). Representations for the Drazin inverse of 2x2 block matrix, SIAM J. Matrix Anal. Appl. 27: 757–771.
CR  - 14.	Li X & Wei Y (2007). A note on the representations for the Drazin inverse of 2x2 block matrices, Linear Algebra Appl. 423: 332–338.
 
15.	Meyer C D & Rose N J (1977). The index and the Drazin inverse of block triangular matrices, SIAM. J. Appl. Math. 33: 1–7.
CR  - 16.	Rao K P S B (2002). The Theory of Generalized Inverses over Commutative Rings, Taylor and Francis, London and New York.
CR  - 17.	Wei Y (1998).  Expression for the Drazin inverse of a 2x2 block matrix, Linear Multilinear Algebra 45: 131–146.
CR  - 18.	Wei Y & Diao H (2005). On group inverse of singular Toeplitz matrices, Linear Algebra Appl.  399: 109–123.
CR  - 19.	Zang H, Cao C & Ge Y (2014). Further results on group inverse of some anti-triangular block matrices, Jour. Applied Math. Comput. 46: 169–179.
UR  - https://dergipark.org.tr/en/pub/ordubtd/issue//441684
L1  - https://dergipark.org.tr/en/download/article-file/502976
ER  -