numericalKernel -- approximate kernel of a matrix

Usage:

V = numericalKernel(M)
Inputs:
- M, a matrix,
Optional inputs:
- Tolerance => ..., default value null, the tolerance of a numerical computation
Outputs:
- V, a matrix,

Description

Computes the kernel of a matrix M numerically using singular value decomposition.

i1 : M = matrix {{1., 1, 1}}

o1 = | 1 1 1 |

                1         3
o1 : Matrix RR    <-- RR
              53        53

i2 : numericalKernel(M, Tolerance=>0.01)

o2 = | -.57735  -.57735  |
     | .788675  -.211325 |
     | -.211325 .788675  |

                3         2
o2 : Matrix RR    <-- RR
              53        53

Singular values less than the tolerance are treated as zero.

i3 : M = matrix {{1., 1}, {1.001, 1}}

o3 = | 1     1 |
     | 1.001 1 |

                2         2
o3 : Matrix RR    <-- RR
              53        53

i4 : numericalKernel(M, Tolerance=>0.01)

o4 = | .70693   |
     | -.707284 |

                2         1
o4 : Matrix RR    <-- RR
              53        53

Ways to use numericalKernel:

numericalKernel(Matrix)

For the programmer

The object numericalKernel is a method function with options.

The source of this document is in /__w/M2/M2/macaulay2-1.26.05+ds/M2/Macaulay2/packages/NumericalLinearAlgebra.m2:240:0.