Khan Academy: Linear Algebra: Transformation Matrix With Respect to a Basis

Video discussing transformation matrices and how a vector is able to be mapped to the same resulting vector by using a transformation matrix with respect to the standard basis as well as one with respect to a different basis. Reviews how a change of basis matrix can be used to find a vector x given the coordinates for x with respect to a basis and vice versa. Then uses that information to find a relationship between the different transformation matrices. [18:02]