Classical groups {unitary group} can preserve complex linear transformations and maintain non-singular Hermitean form, rather than orthogonal-group quadratic form. Hermitean form equals its complex conjugate {Hermitean conjugation}, which is the dual space. For unitary groups, linear-transformation inverse is positive-definite transpose. For pseudo-unitary groups, linear-transformation inverse is not positive-definite transpose.
Mathematical Sciences>Group Theory>Mathematical Groups
3-Group Theory-Mathematical Groups
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Date Modified: 2022.0224