Change of Coordinates Visualizer

See how a fixed point in ℝ² gets new coordinates when you change from one basis to another. The point stays fixed — only the grid and coordinates change.

Bases (V: Initial, U: Final)

V (Initial Basis)

U (Final Basis)

Point [x]𝒱

Animation

Animates the change-of-basis transformation between the two coordinate systems. Resets the animation and restores the default view.
1.0×
Point vector
v₁ / u₁
v₂ / u₂
New axes
Grid
Bases & Change of Coordinates Matrix

Change of Coordinates Matrix S = U⁻¹V

Calculation
Preset Examples