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In this paper, we investigate the importance of column scaling in relatingtwo signed-graphic representations of the same matroid. We used the SageMathematics software to generate many examples of signed-graphic matroids andtheir signed-graphic representations. Our examples show that column scaling issometimes necessary in order to transform one signed-graphic representationinto another; moreover, there exist many collections of signed-graphicrepresentations that row-reduce to the same standard form. We also discuss aninteresting matroid-preserving operation on a signed graph, which we call thecylinder flip, that relates certain pairs of signed-graphic representations ofthe same matroid.

Recognizing signed-graphic matroids: Cylinder flips and the importance of column scaling