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They say that the set S is a subspace of R^n. Is that true? Doesn't c have to be zero in order for S (the hyperplane) to be a subspace?

- Thread starter samh
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They say that the set S is a subspace of R^n. Is that true? Doesn't c have to be zero in order for S (the hyperplane) to be a subspace?

- #2

CompuChip

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Let *n* = 2, *a*_{1} = *a*_{2} = 1. If I rename *x*_{1} = *x* and *x*_{2} = *y*, then according to you only

*x* + *y* = 0

defines a line (hyperplane) but

*x* + *y* = 1

doesn't?

[edit]I see your point. Probably they should write that it is ... isometric (is that the word here? it's just a line through the origin translated by a constant vector) to a genuine co-dimension one subspace[/edit]

defines a line (hyperplane) but

doesn't?

[edit]I see your point. Probably they should write that it is ... isometric (is that the word here? it's just a line through the origin translated by a constant vector) to a genuine co-dimension one subspace[/edit]

Last edited:

- #3

matt grime

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Affine is the word you're looking for: things that look like translations of vector subspaces.

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