# ApCoCoA-1:Num.QR

From ApCoCoAWiki

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[1]*QR[2],3); -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Mat([ [<quotes>0.999</quotes>, <quotes>1.999</quotes>, <quotes>2.999</quotes>], [<quotes>1.999</quotes>, <quotes>2.999</quotes>, <quotes>3.999</quotes>], [<quotes>2.999</quotes>, <quotes>3.999</quotes>, <quotes>4.999</quotes>] ]) -------------------------------

### See also