Given two bases B and C in a vector space V, one can consider two related transformations:
1. The linear transformation T that maps vectors from B to vectors from C.
2. The change of coordinates associated with a change of basis.
In physics, this represents "active" and "passive" viewpoints.
In the second case, we have transformation of coordinate functionals. Choosing an inner product in V, we associate linear functionals with vectors in V. This leads to the adjoint transformation T*.
The applet explores geometric properties of T* in relation to the coordinate systems.
It can be useful for the 2nd course in Linear Algebra.
