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extractLeftLower -- Extract L from the LR decomposition result.

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 = | 9/2 1/2 3/2 |
     | 1/2 1   3/4 |
     | 9/4 3/4 7/4 |

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

o3 = | 9/2 1/2   3/2   |
     | 1/9 17/18 7/12  |
     | 1/2 9/17  47/68 |

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

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

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

o5 = | 9/2 1/2   3/2   |
     | 0   17/18 7/12  |
     | 0   0     47/68 |

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

o6 = | 1   0    0 |
     | 1/9 1    0 |
     | 1/2 9/17 1 |

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

o7 = true

See also

Ways to use extractLeftLower:

  • extractLeftLower(Matrix)

For the programmer

The object extractLeftLower is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/AdjointIdeal.m2:1008:0.