ABSTRACT
Matrices can provide a tangible and easily understood description of many abstract mathematical quantities, including vectors and operators on vectors. This chapter presents a review of matrices. The review would include studies of the close relationship between matrices and vectors. In order to motivate later studies of operators the discussion, the chapter presents in a way which can be readily generalised to similar discussion on operators. There are many situations in mathematics and physics in which one should to manipulate rectangular arrays of real or complex numbers. Mathematicians have investigated what is known as the eigenvalue problem for a long time. Basically one starts with an operation on a set of quantities, be it column vectors, vectors or functions. Unitary matrices are a generalisation of the concept of orthogonal matrices to complex matrices. Real unitary matrices are the same as orthogonal matrices since the adjoint of a real matrix is the same as its transpose.
