SVD
Decomposes any matrix as A = U Sigma V^T. For a 2D transform, V gives input directions, singular values give stretch, and U gives output directions.
Linear algebra visualizer
Matrix Decomposition Lab
Compare how SVD, PCA, and EVD explain a transformation or dataset through directions, scaling factors, and variance.
Input
Enter a 2x2 matrix for singular value decomposition.
Visualization
SVD maps the unit circle to an ellipse. Principal directions become ellipse axes.
Numerical Results
Run analysis to see the decomposition.
PCA
Runs eigendecomposition on a covariance matrix. The largest eigenvalue points to the direction with the most variance.
EVD
Decomposes a square matrix as A = V Lambda V^-1 when enough independent eigenvectors exist. It exposes invariant directions of the transform.