Abstract
In this study, inward matrix products are used to construct a theoretical framework where new space-time structures of arbitrary dimensions can be built up. The mathematical theory, based on inward matrix algebra, allows the derivation and integration of vectors and matrices composed by well-behaved functional elements. Every function element is associated at least to a linearly independent variable connected to such an element. As examples are discussed first the construction of general density functions, followed by the reformulation of the time-dependent Schrödinger equation. A general N-dimensional classical universe is presented, where not only space but also time, mass, energy and other related physical properties acquire an arbitrary hypermatrix structure. In this hypothetical framework scalar values related to physical quantities can be alternatively associated to cosine-like measures in the chosen spaces. Finally, simple problems on special relativity are briefly discussed from this point of view.
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Carbó-Dorca, R. Inward Matrix Product Algebra and Calculus as Tools to Construct Space–Time Frames of Arbitrary Dimensions. Journal of Mathematical Chemistry 30, 227–245 (2001). https://doi.org/10.1023/A:1017931905397
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DOI: https://doi.org/10.1023/A:1017931905397