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

 This article is about a function from ApCoCoA-1.

## Num.QR

Computes the 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.

This command computes the QR-decomposition of a matrix using the external library Lapack, i.e. the matrix A will be decomposed into the product of an orthogonal matrix Q and an upper-right triangular matrix R.

• @param A The matrix to decompose.

• @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]]);
QR := Num.QR(Points);
Dec(QR*QR,3);

-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Mat([
["0.999", "1.999", "2.999"],
["1.999", "2.999", "3.999"],
["2.999", "3.999", "4.999"]
])
-------------------------------
```