QR Decomposition

Factor a matrix as Q R via Gram-Schmidt

Matrix A

A = Q · R
Dimensions
3 × 3
Qᵀ Q = IQ R = A
Q — orthonormal columns
0.857143
‎-0.394286
‎-0.331429
0.428571
0.902857
0.034286
‎-0.285714
0.171429
‎-0.942857
R — upper triangular
14
21
‎-14
0
175
‎-70
0
0
35
Diagonal of R (column lengths)
14 · 175 · 35
Reconstruction error: 1e-28 · Orthonormality error: 3e-30
QR DecompositionBlock diagram showing the 3×3 matrix A factored as Q times R: Q has orthonormal columns and R is upper triangular with its diagonal highlighted.A12-5146167-68-424-41=Q0.86-0.39-0.330.430.900.03-0.290.17-0.94·R1421-140175-700035Q has orthonormal columns · R is upper triangular