eigshow — a scope for linear mapseigshow is a free, interactive visualizer for eigenvectors , eigenvalues , and the singular value decomposition (SVD) of 2×2 matrices — steer a probe vector on the unit circle and watch its eigenvalues, singular values, and condition number update live.<br>eigsvd<br>searching

Matrix A

symmetricshearrotationnear-singularstretchreflection

Readout<br>det3.00<br>trace4.00<br>eigenvalues3.00 , 1.00<br>σ₁ , σ₂3.00 , 1.00<br>κ = σ₁/σ₂3.00<br>well-conditioned — the map treats all directions comparably.

Controls<br>sweep ▸reset x<br>reveal eigenvector axes

x — the probe you steer (on the unit circle) Ax — the response locus of Ax (image of the circle)<br>Hunt for an eigenvector. Drag x around the unit circle and watch Ax. Almost everywhere the two arrows point in different directions — the map rotates as well as stretches. An eigenvector is a direction where Ax is perfectly parallel (or anti-parallel) to x: the arrows line up, no rotation, pure scaling. That scale factor is the eigenvalue — the Rayleigh quotient x·Ax / x·x, shown the instant you lock on. The green ellipse is the image of the whole circle; its two "flattest/fattest" directions are where eigen-alignment tends to live for symmetric A.