Geodesic
Linear fractional transforms of companion matrices
Glasgow mathematical journal, Tome 20 (1979) no. 2, pp. 129-132

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Questions about polynomials can be turned into questions about matrices by associating with the polynomial(over an arbitrary field) its companion matrixwhich has p/an as its characteristic polynomial. This technique is often used in stability theory, as indicated in [1]; companion matrices also occur in the theory of the rational canonical form. 
Young, N. J. Linear fractional transforms of companion matrices. Glasgow mathematical journal, Tome 20 (1979) no. 2, pp. 129-132. doi: 10.1017/S0017089500003839
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[1] 1.Shane, B. A. and Barnett, S., On the bilinear transformation of companion matrices, Linear Algebra and Appl. 9 (1974), 175–184. Google Scholar | DOI

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