Multidimensional Analysis
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http://www.georgehart.com/research/multanal.html  


George W. Hart  
A brief introduction to Multidimensional Analysis, a generalization of linear algebra that incorporates ideas from dimensional analysis. The central idea is that vectors and matrices as used in science and engineering can be thought of as having elements which are not just real (or complex) numbers, but formally have different types, such as length or voltage. Quantities with different types do not form an algebraic field as they are not closed under addition, e.g., 1 meter + 1 volt is undefined. Traditional linear algebra assumes that vectors and matrices are isomorphic to arrays of elements which are closed under addition, and so traditional linear algebra is not formally valid for many applications in science and engineering.  


Levels:  College, Research 
Languages:  English 
Resource Types:  Articles, Books 
Math Topics:  Linear Algebra, Analytic Geometry 
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