Linear algebra of reduced units and discussion of temperature parameters in scientific computations

Scientific equations differ from mathematical equations in that in addition to number, one must associate most of these groups of numbers with a ‘physical dimension’. In practice, the dimensional consistency is intuitively presupposed, and no mathematical theory of scientific equations was developed in detail. The objective here is to develop a formal theory of scientific equations, correlating their physical ‘dimensions’ with mathematical structures in an unambiguous manner; intuitive presuppositions have been cast into axiomatic form. The resulting theory is applied to problems in scientific computing and simulations where reduced units are used, and some novel deductions are made directly from the theory concerning temperature and the Boltzmann factor.