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Abstract
Let A be an m × n matrix of real or complex numbers, and let μ. be a given constant ≥ 1. If A has rank m, it is possible to choose m columns of A such that, if B is the m × m matrix formed by these m columns, all entries of B −1 A are less than or equal to μ in absolute value. Moreover, if μ > 1, it is possible to find m such columns in a number of steps that is polynomial in m and n and inversely proportional to log μ.
*This research was supported in part by National Science Foundation grant MCS 83-00984.
*This research was supported in part by National Science Foundation grant MCS 83-00984.
Notes
*This research was supported in part by National Science Foundation grant MCS 83-00984.