Abstract
Let K be a subspace of R n and let K ⊥ be the orthogonal complement of K. Rockafellar has shown that certain properties of K may be characterized by considering the possible patterns of signs of the nonzero components of vectors of K and of K ⊥. Such considerations are shown to lead to the standard characterization theorem for discrete linear Chebyshev approximation as well as to several results on uniqueness of solutions. A method is given for testing uniqueness of a given solution. A special case related to graph theory is discussed and combinatorial methods are given for solving and testing for uniqueness.
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