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NumericalImplicitization :: numericalNullity

numericalNullity -- numerical kernel dimension of a matrix

Synopsis

Description

This method computes the dimension of the kernel of a matrix with real or complex entries numerically, via singular value decomposition (see SVD).

If σ1 ≥...≥σn are the singular values of M, then to establish numerical nullity we look for the first large gap between two consecutive singular values. The gap between σi and σi+1 is large if σii+1 > Threshold.

The optional input Precondition specifies whether or not the rows of M will be normalized to have norm 1 before computing the SVD. This is useful if the matrix is dense (e.g. for an interpolation matrix), but not if the matrix is sparse (e.g. diagonal).

i1 : numericalNullity(matrix{{2, 1}, {0, 0.001}}, Precondition => false)

o1 = 1
i2 : numericalNullity(map(CC^2,CC^2,0))

o2 = 2

See also

Ways to use numericalNullity :