# qr

QR decomposition.

## Syntax

[Q,R] = qr(A)

[Q,R] = qr(A,econ)

## Inputs

`A`- The matrix to decompose.
`econ`- Economy decomposition flag. Set to 0.

## Outputs

- Q
- Orthonormal matrix.
- R
- Upper triangular matrix.

## Example

Matrix input:

`[Q,R] = qr([1,2,3;4,5,6;7,8,10;11,12,15],0)`

```
Q = [Matrix] 4 x 3
-0.073127 -0.8104 0.56383
-0.29251 -0.46944 -0.78362
-0.51189 -0.12848 -0.038225
-0.8044 0.32614 0.25802
R = [Matrix] 3 x 3
-13.675 -15.357 -19.159
0 -1.0822 -1.6406
0 0 0.47782
```

## Comments

[Q,R] = qr(A) computes matrices Q and R such that A = QR.

QR decomposition is often used for solving over-determined linear least squares equations Ax = b. For the economy decomposition of an MxN matrix A with m>n, Q is MxN and R is NxN.

qr uses the LAPACK routines 'dgeqrf' for real matrices and 'zgeqrf' for complex matrices.