This paper investigates the effect of structure-preserving perturbations on the eigenvalues
of linearly and nonlinearly structured eigenvalue problems. Particular attention is paid to
structures that form Jordan algebras, Lie algebras, and automorphism groups of a scalar product.
Bounds and computable expressions for structured eigenvalue condition numbers are derived for
these classes of matrices, which include complex symmetric, pseudo symmetric, persymmetric, skewsymmetric,
Hamiltonian, symplectic, and orthogonal matrices. In particular we show that under mild
assumptions on the scalar product, the structured and unstructured eigenvalue condition numbers
are equal for structures in Jordan algebras. For Lie algebras, the effect on the condition number of
incorporating structure varies greatly with the structure. We identify Lie algebras for which structure
does not affect the eigenvalue condition number.