ABSTRACT
While this may seem to be intense ad hoc mathematics, it represents what took this author at least 5 years to locate and assemble into the necessary tools to function using the linear combination of atomic orbitals and a sense of how to approach seemingly impossible problems in quantum chemistry. We offer it here as a shortcut for interested undergraduates and auxiliary mathematics as an abbreviated course in linear algebra, which can be useful in a number of areas of chemistry. We will mention that this chapter is usually the end of a nine week (six credit, two semester) course and example 2 is almost always treated and tested.
