Schur-like forms for matrix Lie groups, Lie algebras and Jordan algebras
The paper deals with the matrix Lie groups \({\mathcal O}_{p,q}\) of \(\Sigma_{p,q}\)-unitary matrices and Lie group \(Sp(2n)\) of symplectic matrices. Here \(\Sigma_{p,q}= \left[ \begin{smallmatrix} -Ip &0\\ 0 &Ip \end{smallmatrix} \right]\). Lie and Jordan algebras associated with these groups are considered also. The authors describe structure-preserving similarity transformations to condensed forms for the matrices of the groups. These Schur-like forms, in general, are not diagonal or Schur ones, but display the eigenvalue of the matrices. Matrices in the associated Lie or Jordan algebras inherit the related forms under these transformations. The authors also consider the intersections of the above classes of matrices and present the Schur-like forms for multi-structured matrices that arise in quantum chemistry.
scientific article; zbMATH DE number 1331744
scientific article