Indefinite Inner Product Space - Isotropic Part and Degenerate Subspaces

Isotropic Part and Degenerate Subspaces

Let, be subspaces of . The subspace for all is called the orthogonal companion of, and is the isotropic part of . If, is called non-degenerate; otherwise it is degenerate. If for all, then the two subspaces are said to be orthogonal, and we write . If where, we write . If, in addition, this is a direct sum, we write .

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