NLA Visualization

Comparing geometric perspectives of matrix decomposition.

Elementwise view of how the SVD constructs a transformed vector.

Visualize orthogonalization using standard projections.

Visualize numerically stable orthogonalization.

Visualize QR factorization using Householder reflections in 3D.

Visualize QR factorization using Givens rotations in 3D.

Understand how the pointwise condition number of A varies based on the input vector x.

Visualize matrix perturbation geometry and deduced worst-case amplification.

Understand the geometry of the normal equations projection and how b is projected onto the plane defined by A.

Sensitivity of the least squares solution to matrix perturbations.

Visualizing how a vector converges to the dominant eigenvector.

Visualizing how a vector shrinks toward the origin when the spectral radius is less than 1.

Visualizing the expansion of the Krylov subspace block by block.

Visualizing why CG finishes in n steps while GD zig-zags on an SPD matrix.

Step-by-step explicit QR iteration forming R and RQ.

Step-by-step implicit QR iteration tracking the matrix bulge.

Visualizing why Bulge Chasing is equivalent to Explicit QR.

Full end-to-end QR iteration algorithm for finding eigenvalues.

Visualizing why Cholesky Factorization on SPD matrices doesn't need pivoting.