Change value of a certain index in a list of list Python
List of lists changes reflected across sublists unexpectedly
Showing that the orthogonal projection in a Hilbert space is compact iff the subspace is finite dimensional Suppose that we have a Hilbert Space $H$ and $M$ is a closed subspace of $H$. Let $T\colon H\rightarrow M$ be the orthogonal projection onto $M$.   I have to show that $T$ is compact iff $M$ is finite dimensional.  So if we assume that $M$ is finite dimensional then $\overline{T(B(0,1))}$ is a closed bounded set in a finite dim vector normed space and so it is compact. Which gives that $T$ is compact.  But I am unsure how to prove that if $T$ is compact then $M$ is finite dimensional?  Thanks for any help Why does `htop` show more process than `ps` In ps xf  26395 pts/78   Ss     0:00  \_ bash 27016 pts/78   Sl+    0:04  |   \_ unicorn_rails master -c config/unicorn.rb                                            27042 pts/78   Sl+    0:00  |       \_ unicorn_rails worker[0] -c config/unicorn.rb                                           In htop, it shows up like:   Why does htop show more process than ps? Proving that a normal, abelian subgroup of G is in the center of G if |G/N| and |Aut(N)| are relatively prime. Under what conditions does loot despawn? I have found that when my bags get full and I need to vendor loot I can sometimes leave loot on the ground and return to it.  Other times it seems to disappear almost instantly once I leave the area.  Is the loot despawn time based, based on my distance from the dropped loot, or some other factor(s)? How do I check if a string is a number (float)? What is the best possible way to check if a string can be represented as a number in Python?   The function I currently have right now is:  def is_number(s):     try:         float(s)         return True     except ValueError:         return False   Which, not only is ugly and slow, seems clunky. However I haven't found a better method because calling float in the main function is even worse. Why are two universal objects isomorphic? Browsing some , it is claimed that two universal objects are isomorphic because they admit the identity morphism on themselves. But from two identity morphisms, how would you get an isomorphism between the two? Is there any way to index my Github account to google search. I see that many people's account show up as soon as I type their name, but mine doesn't show up even after I type my name followed by github n search. Inverting direction of mouse scroll wheel Is there a way to make a mouse scroll wheel invert its direction? I'd like to scroll upwards and have that action scroll downwards and vice-versa. There is no setting on the Mouse control panel that makes this possible.   Any pointers to a hack or a particular mouse model that has such a setting would be appreciated. I am using Windows 7. Why isn't an upgrade to 20.04 from 18.04 available yet? Can I make a public directory under a private directory? I have a personal folder /a/b on the server with permission 700. I don't want others to list the contents in /a/b. The owner of /a is root.  Now I need to open the full authorities of directory /a/b/c to all users.  I changed the permission of /a/b/c to 777 but it is still inaccessible for others. Unidentified address in Gmail Many times, when I copy&amp;paste an email address into the "To" field in a Gmail message, it refuses to send the email, saying that “the address has not been identified”. This is very frustrating. Is there any solution other than just manually typing the address? Let $\displaystyle \sum a_n$ be  convergent series of positive terms and set  $\displaystyle b_n=\sum_{k=n}^{\infty}a_k$ , then prove that $\displaystyle\sum \frac{a_n}{b_n}$ diverges.   I could see that $\{b_n\}$ is monotonically decreasing sequence converging to $0$ and I can write $\displaystyle\sum \frac{a_n}{b_n}=\sum\frac{b_n-b_{n+1}}{b_n}$, how shall I proceed further? I have a VB background and I'm converting to C# for my new job.  I'm also trying to get better at .NET in general.  I've seen the keyword "T" used a lot in samples people post.  What does the "T" mean in C#?  For example:  public class SomeBase&lt;T&gt; where T : SomeBase&lt;T&gt;, new()   What does T do? Why would I want to use it? Is Dirichlet function Riemann integrable? I don't want to do this through trial and error, and the best way I have found so far was to start dividing from 1.     $n! = \text {a really big number}$   Ex. $n! = 9999999$   Is there a way to approximate n or solve for n through a formula of some sort?  Update (Here is my attempt):  Stirling's Approximation: $$n! \approx \sqrt{2 \pi n} \left( \dfrac{n}{e} \right ) ^ n$$  So taking the log:     $(2\cdot \pi\cdot n)^{1/2} \cdot n^n \cdot e^{-n}$       $(2\cdot \pi)^{1/2} \cdot n^{1/2} \cdot n^n \cdot e^{-n}$       $.5\log (2\pi) + .5\log n + n\log n \cdot -n \log e$       $.5\log (2\pi) + \log n(.5+n) - n$   Now to solve for n:     $.5\log (2\pi) + \log n(.5+n) - n = r$       $\log n(.5+n) - n = r - .5 \log (2\pi)$   Now I am a little caught up here. Where can I find a list of computers guaranteed to work with Ubuntu? Before I buy my next laptop, I'd like to make sure that it will work perfectly with Ubuntu. Is there a list of completely supported computers anywhere? Where Android apps store data? How did Vader saving Luke turn him to the good side? Couldn't Vader save his son and continue being a Sith Lord? Couldn't he have let Luke go and basically become the Emperor and have the Galaxy to himself? I don't think killing the Emperor to save your son will automatically convert you to the light side. Enlighten me. I have a dictionary of values read from two fields in a database: a string field and a numeric field. The string field is unique, so that is the key of the dictionary.  I can sort on the keys, but how can I sort based on the values?  Note: I have read Stack Overflow question here  and probably could change my code to have a list of dictionaries, but since I do not really need a list of dictionaries I wanted to know if there is a simpler solution to sort either in ascending or descending order. Arduino Boost Converter. Connecting load makes converter non functional