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AdjointIdeal :: extractLeftLower

extractLeftLower -- Extract L from the LR decomposition result.

Synopsis

Description

Returns a left lower triangular matrix formed by the corresponding entries of A and with 1 on the diagonal.
i1 : A=random(QQ^3,QQ^3)

o1 = | 1/4 2   4/3 |
     | 5/3 2   3/2 |
     | 5/4 7/2 4/3 |

              3        3
o1 : Matrix QQ  <--- QQ
i2 : (perm,LR)=LRdecomposition(A,j->-j);
i3 : LR

o3 = | 5/3  2     3/2     |
     | 3/4  2     5/24    |
     | 3/20 17/20 149/160 |

              3        3
o3 : Matrix QQ  <--- QQ
i4 : P=transpose (id_(QQ^3))_perm

o4 = | 0 1 0 |
     | 0 0 1 |
     | 1 0 0 |

              3        3
o4 : Matrix QQ  <--- QQ
i5 : R=extractRightUpper(LR)

o5 = | 5/3 2 3/2     |
     | 0   2 5/24    |
     | 0   0 149/160 |

              3        3
o5 : Matrix QQ  <--- QQ
i6 : L=extractLeftLower(LR)

o6 = | 1    0     0 |
     | 3/4  1     0 |
     | 3/20 17/20 1 |

              3        3
o6 : Matrix QQ  <--- QQ
i7 : L*R==P*A

o7 = true

See also

Ways to use extractLeftLower :