The subject of Linear Algebra, in general, covers a broad range of topics - so broad, in fact, that a full semester or more could be spent on topics related to linear algebra. Our goal in this unit is simply to introduce the standard concepts needed for other subjects in this course. In particular, we will first introduce the basic notation and operations associated with vector and matrix algebra and then focus on systems of linear equations, including both inhomogeneous and homogeneous equations. The homogeneous systems, of course, also lead to the important subject of eigenvalues and eigenvectors of a matrix. The classification of matrices based on the properties of their eigenvalues and eigenvectors is also discussed briefly. Finally, a demo is provided to illustrate how to perform many of the analytical operations outlined in this unit within the Matlab programming language.

Students already familiar with this subject material should quickly browse this lecture material to become comfortable with the specific notation used here and also to become acquainted with performing many common and very useful matrix/vector operations within the Matlab environment. Students weak in this subject are encouraged to study the notes thoroughly and/or to consult your textbook or other reference books on this subject as needed.

The key topics treated here are: