Khan Academy: Linear Algebra: Coordinates With Respect to a Basis

A video lesson showing that vectors in space can be defined by coordinates with respect to a basis. A concrete example is given for a vector in R2. Shows how the vector is defined in traditional Cartesian coordinates and then how it can be defined in new skewed coordinates with respect to the basis of a given subspace in R2. Both types of coordinates are shown graphically. Also describes how the traditional Cartesian coordinates are related to the standard basis. [16:08]