Timeline for Linear independence of functions
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 20, 2019 at 21:10 | comment | added | mohi | Thanks Anthony. I disagree that you need the points not to lie on the same plane. In particular, I think for $\phi$ that is not a polynomial and as long as $x_i=\alpha x_j$ (but $\alpha$ not necessarily positive unlike the question) the above result would hold. | |
| Jul 20, 2019 at 21:08 | comment | added | mohi | Thanks, Pietro. I mean the latter any choice of points assumed not in "co-radial" position | |
| Jul 20, 2019 at 8:39 | comment | added | Anthony Quas | If the $x_1,...,x_n$ lie in an affine hyperplane, you have no chance. Otherwise I would anticipate that the answer is any $\phi$ except a polynomial works. This may be morally true rather than literally true. | |
| Jul 20, 2019 at 6:48 | comment | added | Pietro Majer | So the condition on $\phi$ refers to the given points $x_1,\dots,x_n$. Or do you mean a stronger condition, stating that the functions $\phi(w^Tx_1), \phi(w^Tx_2), \ldots, \phi(w^Tx_n)$ are linearly independent for any choice of points $x_1,\dots,x_n$ (always assumed not in "co-radial" position)? | |
| Jul 19, 2019 at 18:49 | history | asked | mohi | CC BY-SA 4.0 |