eigenvalues-and-eigenvectors

Shows how a 2D linear transform A warps the unit square and sends a vector v to Av. A rotating vector gradually snaps to an invariant direction (an eigenspace line), where Av becomes collinear with v and the scaling factor λ is highlighted. A side panel animates det(A−λI) while scanning λ, marking roots (eigenvalues) where the determinant hits 0.

canvasclick to interact

t=0s

practical uses

01.Stability analysis of dynamical systems (growth/decay along eigendirections)
02.PCA / dimensionality reduction (principal eigenvectors of covariance matrices)
03.Differential equations and vibrations (modes and natural frequencies)

technical notes

Uses a fixed 2×2 matrix with real eigenvalues; eigenvalues computed from trace/determinant, eigenvectors from (A−λI)v=0. Blocky aesthetic via snapped DDA pixel-lines on a 4–8px grid. Animation cycles ~4.2s for v→eigenvector and ~2.8s for λ scanning; includes a direction-match meter using normalized dot(v,Av).

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