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I have a matrix of 0's and 1's, and wish to compute its rank. One approach is to compute an approximate decomposition and return a count of the number of pivots that exceed some small threshold.

Though this will usually equal the rank for a reasonably chosen threshold, the two definitions are not mathematically equivalent. What is the best way to compute according to the mathematical definition of rank?

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  • Simple method: Use Gaussian elimination, make use of the fact that for boolean values, addition corresponds to XOR, and in the end count the number of nonzero rows. – JohnB Jan 03 '16 at 14:50

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