Timeline for Embedding non-orthogonal vectors in a vector space

9 events

when toggle format	what		by	license	comment
Jan 18, 2020 at 11:53	comment	added	user35588		In the limit $\epsilon \to 0$, yes there won't be any more vectors. However if the dimensionality of the vector space is quite large, then a sufficiently small $\epsilon$ would give rise to many vectors. See the answer by @Roman in which he has demonstrated that the number of such vectors actually grows like an exponential of $\epsilon$. I also have a similar result to that, but I want an explicit demonstration of the same.
Jan 17, 2020 at 14:16	history	edited	Kagaratsch	CC BY-SA 4.0	added 37 characters in body
Jan 16, 2020 at 17:40	history	edited	Kagaratsch	CC BY-SA 4.0	added 46 characters in body
Jan 16, 2020 at 17:38	comment	added	Kagaratsch		@MikeY Oh, I see what you mean, one can start with a slightly $\mathcal{O}(\epsilon)$ deformed version of $\vec{e}_i$ vectors, but it does not change the argument. I made some edits to accommodate this.
Jan 16, 2020 at 17:35	history	edited	Kagaratsch	CC BY-SA 4.0	added 233 characters in body
Jan 16, 2020 at 16:57	comment	added	MikeY		I think your statement " the vectors $e⃗_{i}$...must be included in this case as well." is not true, although I agree that the number of vectors is still $n$.
Jan 16, 2020 at 16:37	history	edited	Kagaratsch	CC BY-SA 4.0	added 279 characters in body
Jan 16, 2020 at 16:17	history	edited	Kagaratsch	CC BY-SA 4.0	added 207 characters in body
Jan 16, 2020 at 16:06	history	answered	Kagaratsch	CC BY-SA 4.0