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by thaumasiotes 647 days ago
No, I'm talking about the fact that the space spanned by two vectors is sufficient to contain those vectors. All of the analysis you could ever theoretically want to do on them can be done within that space. If you only have two vectors, you never need to consider a space with higher dimensionality than 2. Each vector is a dimension of the space, and that's it.
1 comments
Chinjut 647 days ago
That is the same thing as what is being said in the comment you are replying "No" to.
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thaumasiotes 647 days ago
No, these are not at all the same claim:

(A) Look at this space. Every point within it can be reached by combining these two vectors.

(B) Look at this space. No point outside it can be reached by combining these two vectors.

Saying that two vectors span a space is claim (A). Saying that the space they span contains them is... much weaker than claim (B), but it's related to claim (B) and not to claim (A).

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