ABSTRACT
This chapter discusses 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. The chapter focuses on algebraic systems and then extend the ideas to systems of differential equations and the matrix eigenvalue problem. A matrix is a collection of numbers, or possibly functions, arranged in a rectangular array and enclosed by square brackets. In particular, the determinant of each of these matrices is equal to the product of the individual determinants of the blocks along the main diagonal. A matrix is a collection of elements arranged in a rectangular array and enclosed by square brackets.
