General & First-year
Linear Algebra Lab
A matrix is just a recipe for where space goes. Drag the four entries and the whole grid shears, rotates, stretches and flips: the basis vectors î → (a, c) and ĵ → (b, d) move, the unit square becomes a parallelogram whose area is the determinant (negative means orientation flipped), and the dashed lines are the eigenvector directions — the special lines the transform only stretches and never rotates. When the matrix is a pure rotation there are no real eigenvectors, and the readout says so.
0.75
Determinant
2.00
Trace
1.50
λ₁
0.50
λ₂
The matrix is just where the basis vectors land: î → (a, c), ĵ → (b, d). The determinant is how much area is stretched (negative = flipped); the dashed lines are eigenvector directions — the ones the transform only stretches, never rotates.
How to use this simulation
A matrix is just a recipe for where space goes. Drag the four entries and the whole grid shears, rotates, stretches and flips: the basis vectors î → (a, c) and ĵ → (b, d) move, the unit square becomes a parallelogram whose area is the determinant (negative means orientation flipped), and the dashed lines are the eigenvector directions — the special lines the transform only stretches and never rotates. When the matrix is a pure rotation there are no real eigenvectors, and the readout says so.
Everything runs in your browser — no sign-up, no download. Change a value and the result updates instantly, so you can build a feel for how each input shapes the outcome. It pairs with Crameleon's practice exams and step sheets when you want to go from intuition to working the problems.