-- -*- M2-comint -*- {* hash: 1432094822 *}

i1 : printingPrecision=2;

i2 : M = map(RR^3, RR^5, (i,j) -> (i+1)^j * 1.0)

o2 = | 1 1 1 1  1  |
     | 1 2 4 8  16 |
     | 1 3 9 27 81 |

                3          5
o2 : Matrix RR    <--- RR
              53         53

i3 : (S,U,V) = SVD(M)

o3 = ({88 }, | -.016 -.4  -.92  |, | -.014 -.038 -.11 -.32 -.94  |)
      {3.9}  | -.21  -.89 .4    |  | -.28  -.41  -.57 -.59 .29   |
      {.8 }  | -.98  .2   -.068 |  | -.74  -.41  .066 .51  -.15  |
                                   | .084  .33   -.81 .47  -.081 |
                                   | -.61  .74   .077 -.27 .062  |

o3 : Sequence

i4 : M' = (transpose U) * M * (transpose V)

o4 = | 88       1.1e-14  2.4e-15  -9.4e-16 9.3e-15  |
     | -6.1e-15 3.9      -9.3e-15 -7.2e-16 -1.8e-15 |
     | -7e-15   -6.1e-15 .8       4.1e-16  4.4e-16  |

                3          5
o4 : Matrix RR    <--- RR
              53         53

i5 : e = 1e-10;

i6 : clean_e M'

o6 = | 88 0   0  0 0 |
     | 0  3.9 0  0 0 |
     | 0  0   .8 0 0 |

                3          5
o6 : Matrix RR    <--- RR
              53         53

i7 : clean_e norm (1 - U * transpose U)

o7 = 0

o7 : RR (of precision 53)

i8 : printingAccuracy = 2

o8 = 2

i9 : M'

o9 = | 88 0   0  0 0 |
     | 0  3.9 0  0 0 |
     | 0  0   .8 0 0 |

                3          5
o9 : Matrix RR    <--- RR
              53         53

i10 : (S', U', V') = SVD(M, DivideConquer => true)

o10 = ({88 }, | -.02 -.4  -.92 |, | -.01 -.04 -.11 -.32 -.94 |)
       {3.9}  | -.21 -.89 .4   |  | -.28 -.41 -.57 -.59 .29  |
       {.8 }  | -.98 .2   -.07 |  | -.74 -.41 .07  .51  -.15 |
                                  | .08  .33  -.81 .47  -.08 |
                                  | -.61 .74  .08  -.27 .06  |

o10 : Sequence

i11 : norm \ ({S', U', V'}-{S, U, V})

o11 = {0, 0, 0}

o11 : List

i12 :