chapter  3
29 Pages

Matrix Analysis

WithRamin S. Esfandiari, Bei Lu

In this chapter, we discuss the fundamentals of matrix analysis, including matrix operations and properties, as well as matrix characteristics such as the rank, the determinant, and the inverse. Matrix analysis plays a particularly important role in the treatment of systems of algebraic and/or differential equations that are coupled, that is, when several unknown variables are involved in several equations in the system model. Also discussed in this chapter is the matrix eigenvalue problem, which plays a key role in the determination of a system’s natural frequencies, as well as the solution process for a system of differential equations. First, we focus on algebraic systems and then extend the ideas to systems of differential equations and the matrix eigenvalue problem.