Concluding Remarks

George W. Hart
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George W. Hart: Columbia University, Department of Electrical Engineering

Chapter 8 in Multidimensional Analysis, 1995, pp 219-221 from Springer

Abstract: Abstract We have begun to explore a new branch of applied mathematics, which includes multidimensional analysis and dimensioned linear algebra, and we have discovered a rich structure of interrelated concepts. The most fundamental aspect of this work is that it harmonizes the previously unconnected ideas of mathematical dimensions and physical dimensions. Scientists and engineers need to work with both notions of multidimensionality simultaneously, and the previously available mathematical tools were not suitable for the task. It is not a linguistic accident that the single term dimension was applied to both of these concepts. The dimension vectors defined here are a form of generalized dimension that naturally subsumes the different kinds of degrees of freedom found in the two traditional notions of dimension.

Keywords: Linear Algebra; Mathematical Object; Mathematical Dimension; Dimension Vector; Dimension Scalar (search for similar items in EconPapers)
Date: 1995
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DOI: 10.1007/978-1-4612-4208-6_9

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