21-241: Matrix Algebra

Description

Linear algebra covers material which is essential to anyone who does any mathematical computation in engineering and the sciences. In application and in class, the subject divides naturally into two parts: computation and formal structure. These are intimately related, but operationally distinct: on the one hand, computations with matrices and linear equations can be made into efficient algorithms, in mental code or in computer code, and, once created, these can be carried out with little attention to the theory. On the other band, in order to understand, to choose and then correctly optimize the applications of linear algebra, it is necessary to see the underlying formal algebraic structure. What does this mean for this course? Your challenge will be to master the algorithmic aspects of the subject, without thinking that this is all that there is to the subject, and to deal with the underlying formal structure by using the concrete model of matrices and vectors as a guide and as a tool.