ABSTRACT
In this work, we give the representations of the Drazin inverse for the partitioned matrix [π΄1π΄2ππ΄3] with π΄1 and π΄3 square and singular under the conditions that ππππ(π΄1)=ππππ(π΄3)=1, πππππ(π΄1)β 0 and πππππ(π΄3)β 0, and then we give the representations of the Drazin inverse for the partitioned πΈπ matrix [π΄1π΄2π΄3π΄4] with π΄1 is square and non-singular under the conditions that ππππ(π΄1)=ππππ([π΄1π΄2π΄3π΄4]), and [π΄1π΄2π΄3π΄4]=[πΌπ]π΄1[πΌπ] where π=π΄3 π΄1β1 and π= π΄1β1π΄2. Also, we give the representations of the Drazin inverse for the partitioned matrix [π΄1π΄2π΄3π΄4] with π΄1 square and singular under the conditions that ππππ(π΄1)=ππππ([π΄1π΄2π΄3π΄4])=1, πππππ([π΄1π΄2π΄3π΄4])β 0.
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