Reach into a coordinate plane and drag the two basis vectors to warp the entire grid until your shape lands exactly on the target.
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How to play
A source shape sits on a coordinate grid alongside a target outline. Moving the two basis vector handles applies a linear transformation to the whole plane, your goal is to morph the shape onto the target.
Drag the orange handle (the i vector) and the teal handle (the j vector) to reshape the grid.
The determinant meter shows the signed area scale of your transformation.
If the two vectors line up, the determinant drops to zero and the matrix goes singular, the grid flattens to a line and you can't win until you pull it back.
Match the target outline to clear the level.
Controls
Desktop: click and drag the two vector handles; use Reset to restore the identity grid and New for a fresh puzzle.
Phone & tablet: drag the handles with your finger, touch is fully supported. Vectors snap to half-integer steps.
Tips & strategy
Think of where each unit square corner should land; the vectors are literally the images of (1,0) and (0,1).
Keep the determinant away from zero, a flat, near-singular grid is a dead end.
A negative determinant means you've flipped the orientation, which is sometimes exactly what the target needs.
What you'll learn
Basis makes change of basis tangible: every drag is a real 2x2 matrix acting on the plane.
Skills: linear algebra, change of basis, matrices, vectors
Best for: advanced high school / college
For parents & teachers: change of basis in linear algebra.
About Basis
Basis makes the abstract idea of a change of basis tangible: every drag is a real 2x2 matrix acting on the plane. It's an original, free browser game with daily and practice modes built around hands-on linear algebra.
A free, original browser game on PlayPendium. No download, no install.
