This visualiser was generated by Claude (Anthropic) for the Linear Algebra 101 course materials. Every pixel that carries information is computed, not drawn. Each grid vertex, each point of the test shape and each point of the unit circle is put through a real matrix–vector product — there is no CSS transform anywhere on this page, which matters, because a page that scaled a picture would look identical and teach nothing. The determinant is ad − bc; the signed area of the image square is computed separately, with the shoelace formula on its four mapped corners, so you can watch the two agree instead of being told they do.

The eigen-analysis branches honestly on the discriminant. Eigenvalues come from the characteristic polynomial λ² − tr(A)λ + det(A), and the sign of tr² − 4 det decides which of three worlds you are in. A rotation has no real eigenvectors and this page says so rather than printing a plausible-looking pair. A repeated eigenvalue is split into the diagonalisable case and the defective case, which has only one eigen-direction — there is a preset for it. Eigenvectors are solved from the null space of (A − λI), not looked up.

Notation follows the course, not a second dialect: m2-l3.html already writes the standard basis as e₁ = [1, 0]^T, e₂ = [0, 1]^T and states that “the columns of A are the images of the standard basis vectors”; m4-l1.html writes A v = λv and det(A − λI) = 0. Transpose is written ^T, as in Module 2. Column-vector convention throughout.

What is NOT computed, and says so where you meet it. The preset matrices are definitions — the standard rotation, the standard projector onto the x-axis, the textbook Jordan block [[1, 1], [0, 1]] — not measurements, and each is labelled. The outline of the “F” test shape is illustrative, hand-authored, and deliberately asymmetric in both axes so that a reflection reads as a reflection instead of as a no-op. Nothing on this page is a measurement of anything; it is arithmetic, and the arithmetic is done rather than imitated.