Composition of binary integral quadratic forms via integral 2 × 2 matrices and composition of matrix classes |
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Authors: | Olga Taussky |
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Affiliation: | a California Institute of Technology, Pasadena, California |
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Abstract: | A treatment by integral matrices is given for composition of pairs of integral quadratic forms with the same discriminant. The forms are associated with a pair of similar 2 × 2 matrices AB with irrational eigen values which generate the maximal order. The most general integral similarity between AB is given by a matrix whose entries are linear forms in two indeterminates with integral coefficients. This matrix is a "compositum" of two factors of the same nature. By equating determinants a composition of two quadratic forms results. The method can be generalized to n × n matrices. |
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