Geodesic
On matrices depending on parameters
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 26 (1971) no. 2, pp. 29-43

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Given a family of matrices smoothly depending on parameters of endomorphisms of a complex linear space, it is shown that there is a normal form to which the family can be reduced by the choice of a base smoothly depending on the parameters. The formulae obtained are applied to the investigation of bifurcation diagrams of families of matrices. 
@article{RM_1971_26_2_a2,
     author = {V. I. Arnol'd},
     title = {On matrices depending on parameters},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {29--43},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_1971_26_2_a2/}
}
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V. I. Arnol'd. On matrices depending on parameters. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 26 (1971) no. 2, pp. 29-43. http://geodesic.mathdoc.fr/item/RM_1971_26_2_a2/