QR decomposition of a matrix. The matrix is decomposed as Q∙R.

Syntax

Q,R = QR(M)

Argument

Name

Description

M

A matrix.

Outputs

Name

Description

Q

The orthonormal matrix of the decomposition.

R

The upper triangle of the decomposition. Same size as M.

Example

Find the QR decomposition of a matrix.

Syntax

M = [1,2,-3;4,5,12;-7,8,14]; // Given matrix

q,r = QR(M);

Result

q =   -0.12309      -0.28949    -0.94923

     -0.49237      -0.81267     0.31169

      0.86164      -0.50574     0.042503

r =   -8.124         4.1851      6.5238

      0            -8.6882    -15.964

      0             0           7.183

Comments

QR decomposition is often used for used for solving over determined linear least squares equations Ax = b.

See Also:

Csky

LU

svd