QR Decomposition Calculator
Decompose matrix A into Q (orthogonal) and R (upper triangular) such that A = QR.
Matrix A
A = QR
Decomposition Successful
Q (Orthogonal Matrix)
0.8571-0.3943-0.3314
0.42860.90290.0343
-0.28570.1714-0.9429
R (Upper Triangular)
14.000021.0000-14.0000
0.0000175.0000-70.0000
0.00000.000035.0000
Verification: Q'Q (should be I)
1.0000.0000.000
0.0001.0000.000
0.0000.0001.000
QR Decomposition
Properties
- Q is orthogonal: Q'Q = I
- R is upper triangular
- A = QR exactly
Applications
- Solving least squares problems
- Computing eigenvalues (QR algorithm)
- Orthogonalization of vectors