Completion of partial matrices to contractions

doi:10.1016/0022-1236(86)90091-1

Journal of Functional Analysis

Volume 69, Issue 2, November 1986, Pages 260-267

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Abstract

An n-by-m partially specified complex matrix is called a partial contraction if every rectangular submatrix consisting entirely of specified entries is itself a contraction. Necessary and sufficient condition are given for the pattern of specified entries such that any n-by-m partial contraction with this pattern may be completed to a full n-by-m contraction.

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^∗: The work of this author was supported in part by National Science Foundation Grant DMS-8500372 and Office of Naval Research Contract N00014-86-K-0012.

^†: The work of this author was supported in part by National Science Foundation Grant DMS-8501794.