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HUANG Xuan-chen, WEI Mu-sheng. New Definitions of Partial Ordering of Generalized Inverse(Chinese)[J]. Journal of East China Normal University (Natural Sciences), 2007, (1): 36-41.
Citation:
HUANG Xuan-chen, WEI Mu-sheng. New Definitions of Partial Ordering of Generalized Inverse(Chinese)[J]. Journal of East China Normal University (Natural Sciences), 2007, (1): 36-41.
HUANG Xuan-chen, WEI Mu-sheng. New Definitions of Partial Ordering of Generalized Inverse(Chinese)[J]. Journal of East China Normal University (Natural Sciences), 2007, (1): 36-41.
Citation:
HUANG Xuan-chen, WEI Mu-sheng. New Definitions of Partial Ordering of Generalized Inverse(Chinese)[J]. Journal of East China Normal University (Natural Sciences), 2007, (1): 36-41.
By using the concept of partial ordering of matrix, some new definitions of partial ordering were put forward, such as $\boldsymbol{A}\leqslant^{\{1\}}\boldsymbol{B}\Leftrightarrow \boldsymbol{A}\boldsymbol{A}\{1\}=\boldsymbol{B}\boldsymbol{A}\{1\},\boldsymbol{A}\{1\}\boldsymbol{A}=\boldsymbol{A}\{1\}\boldsymbol{B} $ and $\boldsymbol{A}\leqslant^{\{1,2\}}\boldsymbol{B}\Leftrightarrow \boldsymbol{A}\boldsymbol{A}\{1,2\}=\boldsymbol{B}\boldsymbol{A}\{1,2\},\boldsymbol{A}\{1,2\}\boldsymbol{A}=\boldsymbol{A}\{1,2\}\boldsymbol{B}$. Four situations were discussed in detail, according to which, sufficient and necessary conditions of the new partial ordering have been derived.
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