Linear Algebra
First-year university, and famously the moment maths stops being about numbers and starts being about space. These demos make the leap concrete: a matrix isn't a table, it's a way of bending the whole plane — and once you see that move, the determinant, complex multiplication and the cross product all become the same idea.
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Matrix Transformations
A 2×2 matrix bends the plane
Drag î and ĵ and watch the whole grid stretch, rotate, shear and flip with them. The two columns of the matrix are where the basis lands — and the determinant is the area of the box they span, negative when space turns inside-out.
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Available now
Complex Numbers & the Argand Plane
Multiplication is rotation
Drag two complex numbers on the plane. Adding them is just sliding one along the other — but multiplying them multiplies the lengths and adds the angles. That single fact is why complex numbers run rotations, waves and AC circuits.
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Available now
Cross Product & 3D Vectors
u × v, perpendicular to both
Set two 3D vectors and spin the scene with your finger. Their cross product stands straight up out of the parallelogram they span — its length is that parallelogram's area, and it points where the right-hand rule says. Zero exactly when the vectors are parallel.
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Related: Vectors & the Dot Product (the cross product's partner) and the Function Transformer (the 1-D cousin of a matrix).