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Use of the concept of physical dimensions in the structural approach to systems analysis

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Abstract

The principle of dimensional homogeneity, which asserts that any system of equations describing a physical phenomenon should be consistent with respect to physical dimensions, is shown to imply a kind of total unimodularity of the physically-dimensioned coefficient matrix of the (linearized) system. This fact can be utilized in the structural approach to systems analysis in a number of ways; for example, it is useful in formulating some problems concerning dynamical systems in matroid-theoretic terms as well as in reducing the computational complexity needed to solve them by combinatorial algorithms.

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Authors and Affiliations

  1. Institute of Socio-Economic Planning, University of Tsukuba, Sakura-mura, 305, Ibaraki, Japan

    Kazuo Murota

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  1. Kazuo Murota
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Murota, K. Use of the concept of physical dimensions in the structural approach to systems analysis. Japan J. Appl. Math. 2, 471–494 (1985). https://doi.org/10.1007/BF03167086

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  • DOI: https://doi.org/10.1007/BF03167086

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