ABSTRACT
Mappings and functions discussed are very general concepts used to relate two sets of quantities. This chapter introduces a special class of mappings known as functionals. An operation which changes the length of a given vector by scalar multiplication and an operation which changes the length as well as the direction of a given vector by projecting it onto another direction. An operator is defined by its effect on vectors. It would be useful to have explicit expressions for operators in terms of familiar quantities. This can be achieved in terms of matrices. Since one should represent vectors by column vectors we should be able to represent operators by square matrices to acting on column vectors. Operators are abstract quantities which do not manifestly possess any numerical values. For physical applications we need numerical values. As with matrices operators can generate numerical values in the form of eigenvalues. Any operator, apart from the identity operator, will affect a vector.
