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Abstract
It is proven that the minimal rank of a partial banded matrix equals the maximum of the minimal ranks of all triangular subpatterns. This proves partly the minimal rank conjecture in a paper by N. Cohen, C. R. Johnson, L. Rodman and H. J. Woerdeman (Operator Theory: Advances and Applications 40 (1989), 165-185).
The results are applied to the problem of simultaneously completing a matrix and its inverse.
∗Partially supported by NASA contract NAS1-18347.
∗Partially supported by NASA contract NAS1-18347.
Notes
∗Partially supported by NASA contract NAS1-18347.