@article{article_441684, title={Some Expressions for the Group Inverse of the Block Partitioned Matrices with an Invertible Subblock}, journal={Ordu Üniversitesi Bilim ve Teknoloji Dergisi}, volume={8}, pages={100–113}, year={2018}, author={Maden, Selahattin}, keywords={Skew field,Block partititoned matrix,Group Inverse of a matrix,Invertible subblock,Drazin inverse}, abstract={<p class="MsoNormal" style="text-align:justify;line-height:11.0pt"> <span lang="EN-US" style="font-family:"Times New Roman",serif; mso-ansi-language:EN-US">  <o:p> </o:p> </span> <span lang="EN-US" style="font-size: 0.9em; font-family: "Times New Roman", serif;">Let </span> <span style="font-size: 11pt; line-height: 115%; font-family: Calibri, sans-serif; position: relative; top: 4.5pt;"> <v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"> <v:f eqn="sum @0 1 0"> <v:f eqn="sum 0 0 @1"> <v:f eqn="prod @2 1 2"> <v:f eqn="prod @3 21600 pixelWidth"> <v:f eqn="prod @3 21600 pixelHeight"> <v:f eqn="sum @0 0 1"> <v:f eqn="prod @6 1 2"> <v:f eqn="prod @7 21600 pixelWidth"> <v:f eqn="sum @8 21600 0"> <v:f eqn="prod @7 21600 pixelHeight"> <v:f eqn="sum @10 21600 0"> </v:f> </v:f> </v:f> </v:f> </v:f> </v:f> </v:f> </v:f> </v:f> </v:f> </v:f> </v:f> </v:formulas> <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"> <o:lock v:ext="edit" aspectratio="t"> </o:lock> </v:path> </v:stroke> </v:shapetype> <v:shape id="_x0000_i1025" type="#_x0000_t75" style="width:8.25pt; height:15pt"> <v:imagedata src="file:///C:/Users/Toshiba/AppData/Local/Temp/msohtmlclip1/01/clip_image001.png" o:title="" chromakey="white"> </v:imagedata> </v:shape> </span> <span lang="EN-US" style="font-size: 0.9em; font-family: "Times New Roman", serif;"> be a skew field and </span> <span style="font-size: 11pt; line-height: 115%; font-family: Calibri, sans-serif; position: relative; top: 4.5pt;"> <v:shape id="_x0000_i1025" type="#_x0000_t75" style="width:28.5pt;height:15pt"> <v:imagedata src="file:///C:/Users/Toshiba/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png" o:title="" chromakey="white"> </v:imagedata> </v:shape> </span> <span lang="EN-US" style="font-size: 0.9em; font-family: "Times New Roman", serif;"> be the set of all </span> <span style="font-size: 11pt; line-height: 115%; font-family: Calibri, sans-serif; position: relative; top: 4.5pt;"> <v:shape id="_x0000_i1025" type="#_x0000_t75" style="width:24.75pt;height:15pt"> <v:imagedata src="file:///C:/Users/Toshiba/AppData/Local/Temp/msohtmlclip1/01/clip_image003.png" o:title="" chromakey="white"> </v:imagedata> </v:shape> </span> <span lang="EN-US" style="font-size: 0.9em; font-family: "Times New Roman", serif;"> matrices over </span> <span style="font-size: 11pt; line-height: 115%; font-family: Calibri, sans-serif; position: relative; top: 4.5pt;"> <v:shape id="_x0000_i1025" type="#_x0000_t75" style="width:10.5pt;height:15pt"> <v:imagedata src="file:///C:/Users/Toshiba/AppData/Local/Temp/msohtmlclip1/01/clip_image004.png" o:title="" chromakey="white"> </v:imagedata> </v:shape> </span> <span lang="EN-US" style="font-size: 0.9em; font-family: "Times New Roman", serif;">  The purpose of this paper is to give some necessary and sufficient conditions for the existence and some expressions of the group inverse of the block matrix  </span> <span style="font-size: 11pt; line-height: 115%; font-family: Calibri, sans-serif; position: relative; top: 9pt;"> <v:shape id="_x0000_i1025" type="#_x0000_t75" style="width:99.75pt;height:24pt"> <v:imagedata src="file:///C:/Users/Toshiba/AppData/Local/Temp/msohtmlclip1/01/clip_image005.png" o:title="" chromakey="white"> </v:imagedata> </v:shape> </span> <span lang="EN-US" style="font-size: 0.9em; font-family: "Times New Roman", serif;">  ( </span> <span style="font-size: 11pt; line-height: 115%; font-family: Calibri, sans-serif; position: relative; top: 4.5pt;"> <v:shape id="_x0000_i1025" type="#_x0000_t75" style="width:6.75pt;height:15pt"> <v:imagedata src="file:///C:/Users/Toshiba/AppData/Local/Temp/msohtmlclip1/01/clip_image006.png" o:title="" chromakey="white"> </v:imagedata> </v:shape> </span> <span lang="EN-US" style="font-size: 0.9em; font-family: "Times New Roman", serif;"> is square) under some conditions, where  </span> <span style="font-size: 11pt; line-height: 115%; font-family: Calibri, sans-serif; position: relative; top: 4.5pt;"> <v:shape id="_x0000_i1025" type="#_x0000_t75" style="width:9.75pt;height:15pt"> <v:imagedata src="file:///C:/Users/Toshiba/AppData/Local/Temp/msohtmlclip1/01/clip_image007.png" o:title="" chromakey="white"> </v:imagedata> </v:shape> </span> <span lang="EN-US" style="font-size: 0.9em; font-family: "Times New Roman", serif;"> be a square block matrix with an invertible subblock.  </span> </p> <p class="MsoNormal" style="text-align:justify;line-height:11.0pt"> <span lang="EN-US" style="font-family:"Times New Roman",serif; mso-ansi-language:EN-US"> <o:p> </o:p> </span> </p>}, number={1}, publisher={Ordu University}