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NumericalHilbert :: colReduce

colReduce -- Column reduces a matrix

Synopsis

Description

Performs Gaussian column reduction on a matrix M, retaining only the linearly independent columns.

i1 : M = matrix {{1., 2, 3}, {2, 4, 0}}

o1 = | 1 2 3 |
     | 2 4 0 |

                2          3
o1 : Matrix RR    <--- RR
              53         53
i2 : colReduce(M, 0.01)

o2 = | 1 0 |
     | 0 1 |

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

Entries with absolute value below the tolerance are treated as zero and not used as pivots.

i3 : N = matrix {{0.001, 0, 0}, {1, 1, 3}, {2, 2, 5.999}}

o3 = | .001 0 0     |
     | 1    1 3     |
     | 2    2 5.999 |

                3          3
o3 : Matrix RR    <--- RR
              53         53
i4 : colReduce(N, 0.01)

o4 = | 0       |
     | 1       |
     | 1.99967 |

                3          1
o4 : Matrix RR    <--- RR
              53         53

Ways to use colReduce :