ABSTRACT
Matrices and linear algebra are indispensible tools for analysis and computation in problems involving systems and control. This chapter presents an overview of these subjects that highlights the main concepts and results. Using the interpretation of the rows and the columns of a matrix as matrices themselves, several important observations follow from the defining equation for the elements of a matrix product. Many properties of determinants can be verified directly from the Laplace expansion formulas. Inversion of upper and lower triangular matrices is done by a simple process of back-substitution; the inverses have the same triangular form. For matrices whose elements may possibly be complex numbers, a generalization of transposition is often more appropriate. When matrices are viewed as representations of linear functions, it is more appropriate to employ a different kind of norm, one that arises from the role of a linear function as a mapping between vector spaces.
