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Eigenvalue and eigenvector derivatives of second-order systems using structure-preserving equivalences

This work shows that eigenvalue and eigenvector derivatives for quadratic eigenvalue problems can be viewed very elegantly and generally from a radically new perspective. The paper contains the first revelation of a new definition for the quadratic eigenvalue problem - the "Dilated Form". This form is now well known among the matrix polynomial community - particularly through the EPSRC-funded matrix operators and pencil network (Marco.Marletta@cs.cardiff.ac.uk). These insights into the quadratic eigenvalue problem feature centrally in the (mathematics) research fellowship (EP/I005293/1) held by FTisseur@maths.manchester.ac.uk .