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Macaulay2 web site
NumericalAlgebraicGeometry
::
numericalRank
numericalRank -- numerical rank of a matrix
Synopsis
Usage:
r = numericalRank M
Inputs:
M
, a matrix with real or complex entries
Optional inputs
:
Threshold => ...
, -- numerical rank of a matrix
Outputs:
r
Description
Find an approximate rank of the matrix
M
by finding the first large 'gap' between two consecutive singular values. The gap between sigma_i and sigma_{i+1} is large if
sigma_i/sigma_{i+1} > Threshold
.
i1 : numericalRank matrix {{2,1},{0,0.001}} o1 = 1
Caveat
sigma_0=1 is assumed
See also
SVD
-- singular value decomposition of a matrix
Ways to use
numericalRank
:
numericalRank(Matrix)