Matrices & linear transforms

LINEAR TRANSFORMATION SIMULATION

▸ Building the coordinate grid & basis vectors î, ĵ…

▸ Loading the target matrix [[a, b], [c, d]]

▸ Interpolating smoothly: identity matrix → target matrix

▸ Computing the determinant det = ad − bc (area factor)

▸ Solving eigenvalues λ & drawing eigenvectors…

▸ Ready — Online. ✅

Matrix & invariants

▦ 2×2 matrix

î (green) · ĵ (red) · unit cell → image

î → (a, c)—

ĵ → (b, d)—

Determinant det—

Trace—

Eigenvalue λ₁—

Eigenvalue λ₂—

Tip

Column 1 = where î lands, column 2 = where ĵ lands. det = ad − bc is the signed area-scaling factor (negative = flips like a mirror). An eigenvector = a direction that does not change, only stretched by λ.

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Switch the Scenario to see different grid transforms (rotate · scale · shear · reflect · singular · project) · click a structure to open a card

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det · λ₁ · λ₂ over the morph progress (0 → target → 0) detλ₁λ₂