QR decomposition in 2D
In this example, the matrix A is written as A = QR. The upper triangular factor R shears and rescales the grid, while the orthogonal factor Q rotates it without changing lengths or angles.
QR Decomposition — Geometric Interpretation in 2D and 3D
This page shows two visual examples of QR decomposition in 2D and 3D. In each case, the factorization is presented as a composition of an upper triangular transformation followed by an orthogonal transformation.
QR decomposition in 3D
The same structure appears in three dimensions. Here the factor R produces an upper triangular transformation, and the factor Q applies an orthogonal transformation, separating deformation from rigid motion.
Related visual: Gram-Schmidt Orthogonalization — Stepwise Visualization in 2D and 3D
Related chapter: QRF, Gram-Schmidt, part 1
Related work: GraphMath Linear Algebra
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