Generating a d-dimensional linear subspace efficiently

Authors:
Raphael Yuster
Affiliations:
University of Haifa, Haifa, Israel
Venue:
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Year:
2010

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Abstract

We present an algorithm for computing a d-dimensional subspace of the row space of a matrix. For an n x n matrix A with m nonzero entries and with rank(A) ≥ d the algorithm generates a d x n matrix with full row rank and which is a subspace of Rows(A). If rank(A) d the algorithm generates a rank(A) x n row-equivalent matrix. The running time of the algorithm is [EQUATION] where ω A, and hence the computation of rank(A), in time [EQUATION] We note that the running time is sub-quadratic if d n2/m)0.528.