John M. Erdman wrote:This set of notes is an activity-oriented introduction to the study of linear and multilinear algebra. The great majority of the results in beginning linear and multilinear are straightforward and can be verified by the thoughtful student. Indeed, that is the main point of these notes— to convince the beginner that the subject is accessible. In the material that follows there are numerous indicators that suggest activity on the part of the reader: words such as "proposition", "example", "exercise", and "corollary", if not followed by a proof or a reference to a proof, are invitations to verify the assertions made. When the proof of a theorem appears to me to be too difficult for the average student to (re)invent and I have no improvements to offer to the standard proofs, I provide references to standard treatments. These notes were written for a 2-term course in linear/multilinear algebra for seniors and first year graduate students at Portland State University. 

The prerequisites for working through this material are quite modest. Elementary properties of the real number system, the arithmetic of matrices, ability to solve systems of linear equations, and the ability to evaluate the determinant of a square matrix are assumed. A few examples and exercises depend on differentiation and/or integration of real valued functions, but no particular skill with either is required.