| 11. | For each infinite-dimensional subspace X _ 0 of X.
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| 12. | However it is possible for infinite dimensional subspaces to be finite.
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| 13. | A linear subspace W \ subset V is called "'
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| 14. | Also, every infinite-dimensional subspace of is finitely universal.
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| 15. | There are two subspaces that are closed respect to the product.
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| 16. | The 1 degree of freedom is the dimension of this subspace.
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| 17. | Linear subspaces, flats were not available to me for explanation.
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| 18. | Generators for this invariant subspace are denoted by q, t.
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| 19. | Invariant subspaces have importance besides finite-dimensional group representation theory.
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| 20. | Modern examination of the commutator subspace involves checking its spectral characterisation.
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