The dimensions of physical quantities q are interpreted as vectors qi(γi1, γi2, …,γin)≡γi1b1+γi2b2+…+γinbn, where the basic elements bj generating the vector space represent the basic quantities of the dimensional system and the coefficients γj are defined by an equation. This interpretation permits the application of the theorems on vector spaces to dimensional analysis. Some results of this approach are simplified rules for the transformation of dimension and unit systems and a physically more transparent derivation of a complete set of dimensionless products by a transformation of bases. The new notation yields a sequential order of physical equations which may lead to a dimensional analysis based on appropriately selected equation groups.
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IBM Journal of Research and Development
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06 April 2010
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