The linear algebra learner
toolbox.
Inspect matrix factors, nullspaces and iterative solution traces.
8 useful places to start.
Small numeric matrices make the conventions visible. Factorisations are approximate, with explicit singularity thresholds.
Small matrix calculator
Add, multiply, transpose, invert or find a determinant for matrices up to 6 × 6.
Row reduction, rank & nullspace
Reduce a small matrix and inspect pivot columns, numerical rank and nullspace basis.
2 × 2 eigenvalue calculator
Find real or complex-conjugate eigenvalues of a real 2 × 2 matrix.
Cholesky decomposition
Factor a small symmetric positive-definite matrix as L times its transpose.
Pivoted LU decomposition
Inspect lower and upper triangular factors and the row permutation.
QR decomposition
Factor a small matrix into an orthonormal basis and upper-triangular coefficients.
Iterative linear-system solver
Trace Jacobi or Gauss–Seidel iterations and inspect residual convergence.
3D vector calculator
Calculate lengths, dot and cross products, angle and vector projection.
A few things you
can tick off.
- Check matrix reconstruction
- Inspect a nullspace basis
- Compare iteration residuals