ABSTRACT
This chapter discusses a systematic matrix formulation of vector algebra, referred to as algebraic vector representation. It assumes that the reader has the fundamental knowledge of vector and matrix algebra. The reference axis may be a stationary or a moving axis; it may be an axis of a reference frame or another vector. Compact matrix notation often allows one to concentrate on the form of a system of equations and what it means, rather than on the minute details of its construction. Matrix manipulation also allows for the organized development and simplification of systems of equations. The row rank of a matrix A is defined as the largest number of linearly independent rows in the matrix. In the kinematics and dynamics of mechanical systems, vectors representing the position of points or bodies, or quantities describing the geometry of the dynamics of the motion, are often functions of time or some other variables.
