Complementarity properties of Peirce-diagonalizable linear transformations on Euclidean Jordan algebras
Peirce-diagonalizable linear transformations on a Euclidean Jordan algebra are of the form L(x) = A . x := Sigma a(ij)x(ij), where A = [a(ij)] is a real symmetric matrix and Sigma x(ij) is the Peirce decomposition of an element x in the algebra with respect to a Jordan frame. Examples of such transformations include Lyapunov transformations and quadratic representations on Euclidean Jordan algebras. Schur (or Hadamard) product of symmetric matrices provides another example. Motivated by a recent generalization of the Schur product theorem, we study general and complementarity properties of such transformations.
euclidean jordan algebra quadratic representation peirce-diagonalizable transformation linear complementarity problem symmetric cone schur/hadamard product lypaunov transformation