A Theoretical Framework for Matrices with Dynamic Dimensions: Formalization and Applications
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In this paper, we present a novel theoretical framework for analyzing matriceswhose dimensions evolve according to convergent or divergent sequences. This approach extends classical matrix theory and enables modeling of dynamic systemswhere the number of parameters or components is not fixed. We define fundamentaloperations on such objects, explore the topological and spectral properties of dynamic matrix spaces, and develop a convergence theory for these objects. We presentapplications in various fields including growing network analysis, econometrics, signal processing, and quantum mechanics. This paper establishes the foundationsfor further research on matrices with dynamic dimensions and their applications inmathematical modeling of complex systems.
