A Matrix Representation of Classical Electromagnetism: Computational Advantages of M3(C) Structure

Abstract: This publication presents a matrix-based computational framework for classical electromagnetism, mathematically equivalent to standard Maxwell equations. The formulation embeds the dimensionally consistent field f = E + icB into traceless anti-Hermitian matrices in M3(C), enabling compact data layout and efficient use of modern SIMD/GPU architectures. Rationale for This Version: This work intentionally separates the M3(C) representation from the broader meta-theoretical context introduced in the author's previous publication (DOI: 10.5281/zenodo.18439269). The purpose of this separation is practical: to allow the computational and engineering merits of the matrix formulation to be evaluated independently of its deeper algebraic origins. By presenting the method strictly within the established boundaries of classical electromagnetism and linear algebra, this version provides a low-resistance interface for practitioners who wish to assess its numerical and structural advantages without engaging with the underlying theoretical framework. Core Enhancements in This Version: Pragmatic Reframing: All Cognitional Mechanics (CM)-specific terminology has been removed to focus on the computational benefits of the M3(C) representation. Dimensional Rigor: The formulation maintains strict SI consistency through the use of f = E + icB, distinguishing it from the traditional Riemann-Silberstein vector. Computational Logic: The embedding into traceless anti-Hermitian matrices enables efficient memory access patterns, contiguous field storage, and natural alignment with BLAS/GPU kernels.