Chapter 49
Matrix Completion Problems
Luz M. DeAlba
Drake University
Leslie Hogben
Iowa State University and American Institute of Mathematics
Amy Wangsness Wehe
Fitchburg State University
A partial matrix is a rectangular array of numbers in which some entries are specified while others are free to be chosen. A completion of a partial matrix is a specific choice of values for the unspecified entries. A matrix completion problem asks whether a partial matrix (or family of partial matrices with a given pattern of specified entries) has a completion of a specific type, such as a positive definite matrix. In some cases, a “best” completion is sought.
Matrix completion problems arise in applications whenever a full set of data is not available, but ...
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