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- W145874197 abstract "Let $$ {C_{N + 1}} = Cx ldots xC,;N + 1,factors $$(8.1)be the complex number space of N + 1 dimensions. Let GL(N+1, C) be the general linear group in N + 1 complex variables, which we identify with the group of all (N+1) × (N+1) non-singular matrices with complex elements. Suppose GL(n+l,C) acts on CN+1 to the right, as described by $$ left( {{z^0}, ldots ,{z^N}} right) to left( {{z^0}, ldots ,{z^N}} right)g,;gGLleft( {n + l,C} right) $$(8.2)Among the subgroups of GL(N+1, C) are: (1) the unitary group U(N+1), which consists of all matrices g satisfying $$ {t_{gbar g}} = I $$(8.3)where I is the identity matrix; (2) the group GL(k+1, N-k, C), consisting of all non-singular matrices of the form $$ left( {underbrace {begin{array}{*{20}{c}} x x end{array}}_{k + 1},underbrace {begin{array}{*{20}{c}} 0 x end{array}}_{N - k}} right),begin{array}{*{20}{c}} {} ,k + 1} {} ,N - k} end{array} $$(8.4)where the elements at the upper-right corner are zero. The group GL(k+l, N-k, C) is the subgroup of all elements of GL(N+1, C) leaving fixed the (k+1)-dimensional subspace of CN+1 spanned by the first k+1 coordinate vectors." @default.
- W145874197 created "2016-06-24" @default.
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- W145874197 date "1979-01-01" @default.
- W145874197 modified "2023-09-23" @default.
- W145874197 title "The Grassmann Manifold" @default.
- W145874197 doi "https://doi.org/10.1007/978-1-4684-9344-3_8" @default.
- W145874197 hasPublicationYear "1979" @default.
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