Documentation

This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

Compute QR Factorization

MuPAD® notebooks are not recommended. Use MATLAB® live scripts instead.

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

The QR factorization expresses an m×n matrix A as follows: A = Q*R. Here Q is an m×m unitary matrix, and R is an m×n upper triangular matrix. If the components of A are real numbers, Q is an orthogonal matrix. To compute the QR decomposition of a matrix, use the linalg::factorQR function. For example, compute the QR decomposition of the 3×3 Pascal matrix:

P := linalg::pascal(3):
[Q, R] := linalg::factorQR(P)

The product of Q and R gives the original 3×3 Pascal matrix:

testeq(P = Q*R)

Also, you can perform the QR factorization for matrices that contain complex values. In this case, the matrix Q is unitary:

B := matrix([[I, -1], [1, I]]):
[Q, R] := linalg::factorQR(B)

Again, the product of Q and R gives the original matrix B:

testeq(B = Q*R)

Was this topic helpful?