Abstract
An m × n zero-nonzero pattern A with the Hall property allows a full rank matrix A ϵ A with a QR factorization. The union of patterns occurring in Q over all such A is denoted by Q . By further restricting A to have the strong Hall property, a Hasse diagram that is a forest is used to characterize patterns A that yield Q = A , thus preserving the sparsity of A . For fixed n, the sparsest n × n such patterns are characterized by a binary rooted tree.
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