QR decomposition

### 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
| ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦