Author： Tian Y.
Publisher： Taylor & Francis Ltd
ISSN： 0308-1087
Source： Linear and Multilinear Algebra, Vol.50, Iss.2, 2002-03, pp. : 125-131
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Abstract
The minimum rank of the 3 × 3 partial block matrix $$ left[ {matrix{ {A_{11} } & {A_{12} } & ? cr {A_{21} } & ? & {A_{23} } cr ? & {A_{32} } & {A_{33} } cr } } right]$$ is determined when Aij (1 
i, j 3) are all nonsingular matrices of the same size. This solves partially a problem that was proposed in [N. Cohen, C.R. Johnson, L. Rodman and H.J. Woerdeman (1989). Ranks of completions of partial matrices. Operator Theory: Advances and Applications, 40, 165-185.].
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