SVD
Decomposes any matrix as \(A=U\Sigma V^{\mathsf T}\). For a 2D transform, \(V\) gives input directions, singular values give stretch, and \(U\) gives output directions.
Matrix Decomposition Lab
Explore SVD, PCA, and EVD through one focused input, one visualization, and the key numbers.
2 · See what happens
The transformation
SVD maps the unit circle to an ellipse. Principal directions become ellipse axes.
StartUnit circle
ApplyMatrix A
ResultTransformed ellipse
Column 1 of A is the purple arrow A e₁. Column 2 is the cyan arrow A e₂.
3 · Read the result
What the decomposition found
Run analysis to see the decomposition.
What to look for
SVD separates rotation from axis scaling. Compare the singular values to see whether one direction is stretched more strongly.
\(A=U\Sigma V^{\mathsf T}\)
Mode: SVDPrimary strength: —Secondary strength: —Interpretation: —
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.