ABSTRACT
A simple operation is to lengthen or to shorten a vector by a factor a without changing its orientation. The simplest operator of this kind is the identity operatorII^. The operators introduced so far have a clear geometric meaning. One should use these operators as building blocks to establish other operators which may not have distinctive geometric properties. The building blocks we have in mind are projectors. Selfadjoint matrices and selfadjoint operators have many distinctive properties which are crucial to the probabilistic formulation of quantum mechanics. Since selfadjoint operators are represented by selfadjoint matrices one can solve their eigenvalue problem in terms of their representative selfadjoint matrices to obtain similar results, e.g., the contents of Theorems for selfadjoint matrices also carry over to selfadjoint operators. Selfadjoint operators with non-negative eigenvalues can be singled out to form a distinctive group with many useful properties.
