 
 
 
15.3.4  LQ decomposition (HP compatible)
The LQ decomposition of a matrix A is A=LQP, where L is lower
triangular the same size as A (if A is not square, then
ℓi,j=0 for i>j), Q is an orthogonal matrix, and P is a
permutation matrix.
The LQ
command finds the LQ decomposition of a matrix.
- 
LQ takes
A, a matrix.
- LQ(A) returns a list [L,Q,P] of the matrices
given by the LQ decomposition.
Examples
| L,Q,P:=LQ([[4,0,0],[8,-4,3]]) | 
|  | | |  | ⎡ ⎢
 ⎢
 ⎣
 | | ⎡ ⎢
 ⎣
 | | 4.0 | 0.0 | 0.0 |  | 8.0 | 5.0 | −4.4408920985×10−16 | 
 | ⎤ ⎥
 ⎦
 | 
 | , | | ⎡ ⎢
 ⎢
 ⎣
 | | 1.0 | 0.0 | 0.0 |  | 0.0 | −0.8 | 0.6 |  | 0.0 | −0.6 | −0.8 | 
 | ⎤ ⎥
 ⎥
 ⎦
 | 
 | , |  | ⎤ ⎥
 ⎥
 ⎦
 | 
 |  |  |  |  |  |  |  |  |  |  | 
 | 
| L,Q,P:=LQ([[24,18],[30,24]]) | 
In the above examples, LQ=PA.
 
 
