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
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i2 : (perm,LR)=LRdecomposition(A,j->-j);
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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
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i4 : P=transpose (id_(QQ^3))_perm
o4 = | 0 1 0 |
| 0 0 1 |
| 1 0 0 |
3 3
o4 : Matrix QQ <--- QQ
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i5 : R=extractRightUpper(LR)
o5 = | 5/3 2 3/2 |
| 0 2 5/24 |
| 0 0 149/160 |
3 3
o5 : Matrix QQ <--- QQ
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i6 : L=extractLeftLower(LR)
o6 = | 1 0 0 |
| 3/4 1 0 |
| 3/20 17/20 1 |
3 3
o6 : Matrix QQ <--- QQ
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i7 : L*R==P*A
o7 = true
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