ABSTRACT
The methods of linear algebra have been applied in many different fields. The Jordan normal form turns out to be of use in solving linear differential equations, and the simultaneous reduction of quadratic forms can be used to simplify mechanical problems. This chapter deals with a method of obtaining the inverse matrix as the sum of a convergent series and an operator treatment of linear difference equations. The derivative of a function is essentially a linear mapping. The chapter considers a homogeneous system of linear differential equations with variable coefficients. It will be convenient to use a dash rather than a dot to indicate the derivative. The simultaneous reduction of two quadratic forms has an important application in mechanics, to finding the normal modes of vibration of a mechanical system.
