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For Students · Eigenvectors

Eigenvectors for a Fourier series

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a Fourier series live below — adjust the inputs and watch it respond, right in your browser.

Eigenvector VisualizerLive

2×2 linear transformation

Controls

A matrix warps the unit circle into an ellipse. Eigenvectors are the special directions that only stretch — never rotate — by their eigenvalue.

Presets

▶ Run in Python

Data Inspector

det3.00

trace4.00

λ₁3.00

λ₂1.00

Governing equation

A = [2.0 1.0 1.0 2.0], A v = λ v, det (A - λ I) = 0, λ = 3.00, 1.00

Reading this result: Symmetric matrix (b = c): its eigenvectors meet at right angles, so the ellipse axes line up exactly with the green and pink lines.

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Frequently asked questions

Is this good for students?: Yes — this version of "Eigenvectors for a Fourier series" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.