About VectorForge
Most people meet matrices as grids of numbers to multiply. VectorForge shows what a matrix is: a linear transform of the plane. Feed it a shape and it rotates, stretches, shears, reflects, or flattens it — and the same rule that moves one corner moves every point.
Three ideas make it click, and you can watch each one:
- The matrix acts by multiply-and-add — predict where a point lands, then the engine computes it exactly.
- The determinant is the area factor — how much bigger the shape gets. A determinant of 0 means a whole direction was lost (you can’t undo it); a negative determinant means it was flipped.
- Eigenvectors are the directions that don’t turn — the arrows that keep pointing the same way, only stretched. A real rotation has none: everything turns.
This is the on-ramp to the maths behind AI: a matrix is the simplest linear layer of a neural network. What you see here — transform, scale, the directions that survive — is exactly how models compute, just in more dimensions.
The transforms you can try: Rotate · Stretch · Shear · Reflect (x-axis) · Project (flatten) · Zoom · Reflect (y-axis) · Reflect (diagonal) · Shear (vertical) · Squeeze.
Honest note: VectorForge uses exact 2×2 arithmetic to teach the mechanism. It is a maths visualiser, not a claim about any particular AI system, and it collects nothing — everything runs on this device.