Download PDFOpen PDF in browserCurrent version2 x 2 Integer Matrices: Composition of Binary Quadratic FormsEasyChair Preprint 11692, version 17 pages•Date: January 5, 2024AbstractIn this research paper, we consider 2 x 2 integer matrices and identify interesting binary quadratic forms which naturally arise. Specifically, we consider such symmetric integer matrices and derive compositions of pure binary quadratic forms naturally arising in association with determinant of such matrices. We also, discover number-theoretic results associated with trinary quadratic forms naturally arising in connection with 2 x 2 symmetric integer matrices. We formulate a “generalized Waring problem” using real quadratic algebraic numbers. We also discuss composition of binary quadratic forms naturally arising in other interesting structured 2 x 2 integer matrices. We explore representation of integers using trinary as well as binary quadratic forms. Keyphrases: Genus Theorem, eigenvalues, integer matrices, quadratic forms
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