### 15.3.2 QR decomposition

The QR decomposition of a square matrix A is A=QR, where Q is an orthogonal matrix (QTQ=I) and R is upper triangular. The qr command finds the QR decomposition of a matrix.

- qr takes A, a numeric square matrix.
- qr(A) returns a list [Q,R] with Q and R from the QR decomposition.

#### Examples

A:=[[3,5],[4,5]]:; qr(A)

⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣

3
5

4
5

4
5

−

3
5

⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦

,

⎡
⎢
⎣

5 | 7
0 | 1

⎤
⎥
⎦

qr([[1,2],[3,4]])

⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣

1

√

10

3

5

√

10

5

3

√

10

−

1

5

√

10

5

⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦

,

⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣

√

10

7
5

√

10

0

√

10

5

⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦