MatrixRank
 Usage
Notes
 Further Examples
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The rank of a matrix of exact numbers is computed by row reduction.
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The rank of a matrix of inexact numbers can be computed by taking the length of the list of positive singular values of the matrix.
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Using the option Tolerance gives a different result.
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The difference is due to the algorithm, which generates roundoff errors. Usually Mathematica replaces small numbers of order $MachineEpsilon with  unless Tolerance is set to  .
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Sometimes using higher precision will help to correctly determine the rank.
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The rank of a matrix is the difference between the dimension of the range and the dimension of the null space.
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MatrixRank works with symbolic matrices.
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MatrixRank also works with complex matrices.
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You can set Tolerance to be large.
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