# Difference between revisions of "ApCoCoA-1:Num.QR"

## Num.QR

QR-decomposition of a matrix.

### Syntax

```Num.QR(A:MAT):[Q:MAT,R:MAT]
```

### Description

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.

Calculates the QR decomposition of a matrix using Lapack.

• @param A Matrix A

• @return An orthogonal matrix Q and an upper-right triangular matrix R such that Q*R=A.

#### Example

```Points:=Mat([[1,2,3],[2,3,4],[3,4,5]]);
Num.QR(Points);
-------------------------------
[Mat([
[-601818814743685/2251799813685248, 11221204152260750623490098342212473544619072342960407833413029/12855504354071922204335696738729300820177623950262342682411008, 47271922480373450167411707109523238704832584221077416524231372166340777774771/115792089237316195423570985008687907853269984665640564039457584007913129639936],
[-21682807918593711888147761857797/40564819207303340847894502572032, 50535810838769898760508425874290037828518802391596092889928280803858452207141/231584178474632390847141970017375815706539969331281128078915168015826259279872, -1703150499741573022389535271505216648161852967701209661846360168011288983405834487511405397453/2085924839766513752338888384931203236916703635113918720651407820138886450957656787131798913024],
[-16262105938945284629515478500581/20282409603651670423947251286016, -50535810838769832038494686341702987883818294138398199855497298160515307568635/115792089237316195423570985008687907853269984665640564039457584007913129639936, 425787624935393028634420116827871332361842515189763323298971758853897488257161264158457298771/1042962419883256876169444192465601618458351817556959360325703910069443225478828393565899456512]
]), Mat([
[-8425463406411593/2251799813685248, -1504547036859213/281474976710656, -7823644591667907/1125899906842624],
[0, 5896596054914343/9007199254740992, 5896596054914343/4503599627370496],
[0, 0, 1197/9223372036854775808]
])]
-------------------------------
```