This sandbox was generated by Claude (Anthropic) for the Linear Algebra 101 course materials, and is built for Module 9 (Numerical Linear Algebra). Type the entries of a 2×2 or 3×3 matrix A — or pick a preset — and watch the module's numerical quantities update at once: the condition number κ(A) = σmax / σmin, the two iterative solvers (Jacobi and Gauss–Seidel) for A x = b with their convergence trace and the spectral radius ρ(M) of each iteration matrix, and how ill-conditioning amplifies error. Every number is computed from your entries — never sketched.
The condition number is not a proxy here. It is σmax / σmin, and the singular values are the square roots of the eigenvalues of AᵀA: σmax by power iteration and σmin by inverse power iteration on that Gram matrix. The image of the unit circle is A applied to the circle — an ellipse whose semi-axes are exactly σmax and σmin, so the drawn axis ratio is κ. A solver converges from any start exactly when ρ(M) < 1, and a strictly diagonally dominant A guarantees it.
Notation follows the course: column vectors, m × n = rows × columns, the system A x = b, the split A = D + L + U, and the Euclidean norm || · || throughout — the norm the 2‑norm condition number belongs to.
What is chosen rather than computed: the default matrix, the preset matrices (each labelled where it is selected), the perturbation direction, and the extent of the drawn grid. Nothing here is a measurement; it is arithmetic, done rather than imitated.
Course demo — linked from the Module 9 lesson deck; the page itself is English‑only for now. Set a matrix A and a right‑hand side b, then watch the numerics. One thing to take away: the condition number κ(A) is the worst‑case factor by which a relative error in the data is amplified in the answer — and it is the ratio of the largest to the smallest singular value, the same ratio you can see in the axes of the ellipse below.