Faktorisasi Matriks Hermitian Nonkomutatif Berdasarkan Trace

Mira Wadu; Albert Mario  Kumanireng; Arista Marlince  Tamonob

doi:10.29303/griya.v5i4.941

Mira Wadu Universitas Nusa Cendana
Albert Mario Kumanireng Universitas Nusa Cendana
Arista Marlince Tamonob Universitas Nusa Cendana

DOI: https://doi.org/10.29303/griya.v5i4.941

Keywords: hermitian matrix, division ring, trace, dieudonné determinant, matrix factorization

Abstract

This article studies the factorization of Hermitian matrices over a division ring based on their trace values. The main result shows that the trace determines the minimum number of Hermitian factors required in factorization depending on the trace value, namely four factors are sufficient for matrices with zero trace, while for matrices with nonzero trace, one additional diagonalizable factor is required. This result indicates a relationship between additive invariance (trace) and multiplicative invariance (Dieudonné determinant) in noncommutative linear algebra.

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