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Saraski, Silvya Ajeng
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Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Education Materials Science & Nanotechnology Physics

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Cofactor Expansion Approaches for Generalized Determinants of Non-Square Matrices Mulyono, Mulyono; Nasution, Hamidah; Habibi, Rizki; Saraski, Silvya Ajeng
Jurnal Penelitian Pendidikan IPA Vol 11 No 11 (2025): November: In Progress
Publisher : Postgraduate, University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jppipa.v11i11.12335

Abstract

Determinants are conventionally defined only for square matrices, which leaves the theoretical discussion of rectangular matrices relatively undeveloped. This study aims to extend determinant theory by introducing a generalized form of the cofactor expansion applicable to non-square matrices. The method employed in this research is a theoretical–analytical approach that begins with identifying fundamental determinant axioms and proceeds with the construction of a recursive cofactor expansion for   matrices with . Worked examples are used to demonstrate the linearity, antisymmetry under row interchange, and reduction consistency of the proposed formulation when applied to square matrices. The findings indicate that the generalized expansion preserves essential algebraic properties and shows compatibility with established rectangular determinant definitions, including the Radić determinant. Overall, this study provides a coherent theoretical foundation for the generalized determinant of rectangular matrices and contributes to broader applications of determinant-based analysis in linear algebra
Co-Authors Habibi, Rizki Mulyono Mulyono Nasution, Hamidah .