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]

Video first introduces the identity matrix and shows that when any vector is multiplied by the identity matrix the result is the original vector. Also shows that the columns of the identity matrix are called the standard basis for R^n....

Video first introduces the identity matrix and shows that when any vector is multiplied by the identity matrix the result is the original vector. Also shows that the columns of the identity matrix are called the standard basis for R^n....

Video showing that the standard basis is an example of an orthonormal basis. Explains how orthonormal bases make good coordinate systems since they make it easy to find coordinates. A general orthonormal basis is defined and then it is...

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...

Video explains what a basis for a vector subspace is and its criteria: the vectors must span the subspace and be linearly independent. Also gives an informal definition of basis as the minimum set of vectors that spans the subspace....