Timeline for Separable Hilbert space definition doubt
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 1, 2020 at 11:35 | comment | added | Just dropped in | $\mathbb{Q}$ are the rational numbers. Instead of taking the linear span with real coefficients, take the linear span with rational coefficients. this is dense and $\mathbb{Q}$ is countable, which will make the $Q$-span of a countable set countable as well. | |
| Jul 1, 2020 at 11:16 | comment | added | fina | Last doubt @JustDroppedIn, $\mathbb{Q}-span$, I don't understand this. What is $\mathbb{Q}$? | |
| Jul 1, 2020 at 9:56 | comment | added | Just dropped in | @fina I'm afraid I don't have what it takes to discuss these concepts. Sorry! | |
| Jul 1, 2020 at 9:44 | comment | added | Just dropped in | @fina I am confused with these notations, I can't understand what are $X_i(t)$ and what is $L_p$ here? | |
| Jul 1, 2020 at 9:32 | comment | added | Just dropped in | @fina Yes, you can understand these vectors as infinite column matrices and these are indeed scalars. Hilbert dimension is defined in my answer: it is the number of elements that an orthonormal basis has. I hope this helps! | |
| Jul 1, 2020 at 9:32 | vote | accept | fina | ||
| Jul 1, 2020 at 9:30 | comment | added | fina | But then $\langle x,e_{i}\rangle=x_{i}$ are scalar variables, which can be notated either as an infinite matrix, or an infinite vector column, am I right? On the other hand, what is the meaning of "Hilbert dimension"? Do you refer to the dimension of the Hilbert space? And then, I understand that the "nature" of the dimension is given from an index set. However, I don't have that capacity to understand all! But, anyway, fantastic answer! | |
| Jul 1, 2020 at 8:38 | history | answered | Just dropped in | CC BY-SA 4.0 |