ABSTRACT
Matrices and linear algebra are indispensable tools for analysis and computation in problems involving systems and control. This chapter presents an overview of the subjects that highlights the main concepts and results. The determinant of an invertible matrix and the determinant of its inverse are reciprocals. Cramer’s rule is almost never used for computations because of its computational complexity and numerical sensitivity. When a matrix of real or complex numbers needs to be inverted, certain matrix factorization methods are employed; such factorizations also provide the best methods for numerical computation of determinants. Inversion of upper and lower triangular matrices is done by a simple process of back-substitution; the inverses have the same triangular form. The eigenvalues and eigenvectors of real matrices are constrained by conjugacy conditions. The algebra of matrices provides a direct means for defining a polynomial function of a square matrix.
