A video lesson explaining how to change from coordinates with respect to a given basis to traditional Cartesian coordinates and vice versa by using a change of basis matrix. Includes concrete examples in R3. [17:55]

A video lesson explaining how to convert between traditional Cartesian coordinates and coordinates with respect to a given basis by using an invertible change of basis matrix. Includes two concrete examples in R2. [13:34]

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...