ABSTRACT
Vectors are employed extensively in physics. Conceptually we all know what a vector is: a vector is a quantity which has a length (magnitude or norm) as well as a direction. This chapter begins with a summary of the properties of three-dimensional vectors. It focuses on these vectors and their mathematical representations as operators and matrices which provides the intuition for the various concepts and operations of vectors. The chapter examines how it is possible to generate probability distributions in terms of vectors and operators in order to gain an insight into the mathematical framework for the formulation of quantum mechanics. It summarises the properties of three-dimensional vectors in §6.1, §6.2, §6.3 and §6.4. The discussion is organised in a way that can be directly generalised to real and complex vectors in higher as well as lower dimensions.
