CLASSI CATION OF MATRICES AS FINITE ABSTRACT STRUCTURES
Abstract
Abstract
This study examines the regular representations of the nite cyclic groups and over the eld R,
focusing on their construction, spectral properties, and algebraic structure. Explicit representation matrices were generated for each group element, and their closure, associativity, identity,
and inverses were veri ed. Eigenvalue analysis revealed n − th roots of unity as the spectra of
the generator matrices, re ecting the cyclic group structure. The regular representations were
decomposed into direct sums of one-dimensional irreducible components corresponding to the
group characters. Centralizers of the matrices were determined, yielding commutative subrings
within M4(R) and M5(R). Comparative analysis
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