Change of Basis

Coordinates are directions for walking along a grid. Swap the grid and the same arrow gets new numbers — B converts one way, and B⁻¹ converts back.

Step 1 of 22

Speed

v = (1, 2) in the usual coordinates: 1 step along î, 2 along ĵ. Those numbers depend on the grid you measure with. Change the grid and the same arrow gets different numbers.

B =

v =

[v]_B =

The conversion appears once the tour reaches it.

Type into [v]_B and v moves; type into v and [v]_B updates. The columns of B are b₁ and b₂, written in standard coordinates.

DSAverse

Change of Basis

See also

Change of Basis

See also