linear map

• note that a matrix can represent a linear map between vector spaces if a basis is given for each space. See wikipedia

Personal note: I think matrices in linear algebra appear in two places: change of basis and linear maps. And I got the two confused when I was first learning. Depending on how you want to use it, a rotation matrix that goes from \(R^3\) to \(R^3\) can be a linear map or a change of basis.