Maths · Linear algebra · 2×2 & 2D
Work in the plane: multiply 2×2 matrices, read determinant and inverse when it exists, add and scale vectors on a canvas, and optionally stretch by eigenvectors. Back to the maths hub.
For A = [[a,b],[c,d]] and B = [[e,f],[g,h]], the product AB has entries ae+bg, af+bh; ce+dg, cf+dh. Edit either matrix; the product and a geometric view of A acting on the unit square update live.
Gray = unit square. Accent = image under A. Area scale ≈ |det A|.
u + v is tip-to-tail. Drag the tips on the canvas, or edit components. Scale slider multiplies u.
For 2×2 A, solve det(A − λI) = 0: λ² − (tr A)λ + det A = 0. Real eigenvalues give directions that A only stretches (not rotates). The canvas shows those axes when they are real.
Educational 2×2 / 2D linear algebra demo — original wording of standard definitions. Not a full course.