Abstract
While a 2×2 integral matrixA with characteristic polynomialx2-m,m=2,3 (4), and square free, cannot always be expressed as the product of two integral symmetric matrices, it can be expressed as the product of two rational matrices, simultaneously similar to two integral symmetric matrices. This can be achieved in various ways. The paper deals with numerical examples which depend on the 2-part of the ideal class-group attached tox2-m (see earlier work by the author, especially Acta Arith. 24, 151–156 (1973)).
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