If a matrix A square is 0, does it follow that A = 0?
If $A$ is a square matrix and $A^2 = 0$ then $A=0$. Is this true? If not, provide a counter-example.
I have some lines. I want to draw perpendicular lines at the start and end of the lines, on both sides of the lines.  Can somebody help me in Python?  I am using ArcGIS. Installing TTF fonts in LaTeX One of the annoying aspects of LaTeX is the limited number of fonts that come by default, and the pain involved in making new fonts 'LaTeX' ready. I have a collection of truetype fonts that I'd like to prepare for use, and I definitely want to make sure I have vector versions of these fonts (i.e not type 3/bitmapped versions). Is there a relatively painless way to do this ? Interpreting plot.lm() I had a question about interpreting the graphs generated by plot(lm) in R.  I was wondering if you guys could tell me how to interpret the scale-location and leverage-residual plots?  Any comments would be appreciated.  Assume basic knowledge of statistics, regression and econometrics. How can you tell when a sunset is going to be spectacular? I have a spot that I like to take sunset pictures. I find that the most spectacular moments last for only maybe 5-10 minutes. What I would like to do is know about a half hour before that a sunset is going to be spectacular, so I can grab my camera, tripod, walk 5-10 minutes to my sunset spot, set up, and have a few minutes to spare in case something happens. However, I've often missed really cool sunsets, because I just don't know when to photograph them. How can you tell beforehand when a sunset is going to be spectacular? Thanks! was closed as "Not constructive" a little while ago by CasperOne. I'm not here to argue about the closure; in fact, I'm forced to agree that, as it stands, the question is explicitly a polling question and eligible to be closed for that reason.  I'd like to see it preserved, however; it's got a fair bit of useful in-depth information for ObjC/Cocoa developers on the "singleton" topic.* It's also (possibly more importantly) a great duplicate target -- have a look at the list of linked questions. I want to try to stave off deletion, and hopefully get it reopened.** (I did vote for reopening, but it expired.)  My thought is to edit the question itself into a "constructive" form, but after spending some time pondering how to do so, I'm not crazy about any of the ideas that I've come up with. Essentially they all involve reworking the question to fit the answers:   Rewrite the question so that the accepted answer fits exactly. "I've got this singleton implementation, but I really want the creation to happen earlier in my app's execution. How can I make that happen?" This is artificial and (in my opinion) doesn't make a particularly good question. Make the question still general, but more concrete and focused on the implementation give in the body. "What are the pitfalls associated with this singleton creation procedure? Are there other features that my singleton should have?" This is still skirting the border of discussion->NC, and none of the answers really respond to this exactly. Remove the implementation from the question and just ask for the "best" implementation. This obviously requires coming up with stringent criteria for "best", and, while it would preserve the relationship between the Q and A's best, might not even move it out of NC territory.   I'm looking for suggestions of ways to re-write this so that it can stick around. Alternatively, if you think I should just be advocating for a historical lock, say so.   If you think my basic premise is faulty and don't think the question should be preserved at all, I respectfully request that you just downvote me instead of answering -- I'd prefer not to turn this into an argument about the merits of the question, and I definitely don't want it to become a(nother) "deletionist"/"inclusionist" skirmish (and I am not infrequently ).    *Quite a bit of it unfortunately in comments.  **Historical locking would also be an acceptable solution to me, but it doesn't seem to fit the "controversial" criterion. String concatenation: concat() vs "+" operator How do I run a 'sudo' command inside a script? To do a patch manually I must type this command   sudo ./playback_delete_data_patch.sh 09_delete_old_data_p.sql     There is a space just before the 09:   sudo ./playback_delete_data_patch.sh [space] 09_delete_old_data_p.sql   How can I run this inside a script?  There are also several other commands but this one is giving trouble. Scoring when two triple word squares are covered in one play The word QUAGMIRE is on the board vertically, with the Q on the top row, second column. The next player creates SQUEEZED horizontally, landing the S on the triple word square in the top row, first column, and remaining UEEZED landing to the right of the existing Q, ending with the D on the triple word square in the eighth column. Since two triple word squares are covered in this one placement, how would it be scored?  Letters:   S: 1 Q: 10 U: 1 E: 1 x 2 (double letter) E: 1 Z: 10 E: 1 D: 1   27 Total for letters. Do you then multiply by 3 for the first triple word square, and then multiply that result by 3?  27 X 3 = 81, 81 X 3 = 243  Bonus for all 7 tiles placed:  243 + 50 = 293 I'm getting errors in a matrix equation. When I compile it looks fine, but I'd like to fix them so I don't have to press return for every error at compile time. The code for the equation is:  \begin{equation*}  \begin{bmatrix} U(1,t)  &amp; \cdots &amp; U(n,t) \\  \vdots &amp; \ddots &amp; \vdots \\ O_{n1} &amp; \cdots &amp; O_{nn}  \end{bmatrix} \times \begin{bmatrix} W(1,1)  &amp; \cdots &amp; W(1,n) \\  \vdots &amp; \ddots &amp; \vdots \\  W(n,1) &amp; \cdots &amp; W(n,n)  \end{bmatrix} = \begin{bmatrix}  D(1,t)  &amp; \cdots &amp; D(n,t) \\ \vdots &amp; \ddots &amp; \vdots \\ I_{n1} &amp; \cdots &amp; I_{nn} \end{bmatrix}  \end{equation*}   The errors I'm getting are related to missing $'s inserted. Infinite partition of $\mathbb N$ by infinite subsets I'm using a 5 V / 2 A voltage regulator () without a heatsink. I'm testing the circuit with a microcontroller (PIC18FXXXX), a few LEDs and a 1 mA piezzo buzzer. The input voltage is aprox. 24 VDC. After running for a minute, the voltage regulator starts to overheat, meaning it burns my finger if I keep it there for more than a second. Within a few minutes it starts to smell like it's burnt. Is this a normal behavior for this regulator? What could cause it to heat that much?    Other components used in this circuit:  L1:   R2:   F1: A question about using the "v-ing" verbs To native speakers, normally do you use adverbs to modify these v-ing worlds especially when they are the objects of the verbs?  Like:      I regret swimming hurriedly     Not      I regret hurried swimming.      Right? And what about these two sentences:     I regret stamp-collecting     or     I regret collecting stamps   Besides, when using these words, it still retains the verbal characteristics right? Like:       The house needs a careful cleaning.     has the same meaning with       The house needs carefully cleaning.     or       The house needs to be cleaned carefully.   (SOMETHING like passive voice) Can't access pre populated SQLite database using PhoneGap/Cordova in Android In a Cycles scene I have an equirectangular image serving as an Environment Texture background (set in the World settings).  I have a glossy object being partially lit by the Environment Texture, as well as getting reflections from it.  Is there a way I can exclude the Environment Texture from affecting the glossy object completely? I want the image as background wallpaper only. The glossy object should be affected by other objects and lights within the scene: everything except the Environment Texture. REST API composite query: How do I use the result of a query subrequest in the referenceId of another subrequest? I am using Salesforce's REST API to (1) retrieve a list of object IDs according to a query, then (2) retrieve the records that correlate to those IDs.  I am familiar with the Salesforce composite documentation .    My request looks like this:  POST: /services/data/v48.0/composite  {     "allOrNone":false,     "compositeRequest": [ {         "method":"GET",         "url": "/services/data/v48.0/query?q=SELECT+Id+FROM+My_Entity+WHERE+(CreatedById+!=+'asdfghjkl')",         "referenceId": "myEntity"         },{         "method":"GET",         "url": "/services/data/v48.0/composite/sobjects/My_Entity?ids=@{myEntity.records[0].Id}",         "referenceId":"myObject"     }] }   My response:  {     "compositeResponse" : [ {         "body" : {             "totalSize" : 21,             "done" : true,             "records" : [ {                 "attributes" : {                     "type" : "My_Entity",                     "url" : "/services/data/v48.0/sobjects/My_Entity/a0D6g000xxxxxxx"                 },                 "Id" : "a0D6g000xxxxxxx"                 }, {*record2*}, {*etc*}             ]},             "httpHeaders" : { },             "httpStatusCode" : 200,             "referenceId" : "myEntity"         }, {         "body" : [ {         "errorCode" : "PROCESSING_HALTED",         "message" : "'myEntity.records' references an invalid Datatype. Only Strings and primitive data types are allowed to be referenced from previous operations."         } ],         "httpHeaders" : { },         "httpStatusCode" : 400,         "referenceId" : "myObject"     } ] }   The first subrequest (the query) executes without errors.  My problem is the second subrequest.  I understand from  that I can refer to the ID of a single item (e.g. myEntity.records[0].Id).  Question: How do I use all items from myEntity.records in the second subrequest? $f(z)=\frac{z}{1+|z|} $ Is 1-1? Minimum value of $\left(a+\frac{1}{b}\right)^2+\left(b+\frac{1}{c}\right)^2+\left(c+\frac{1}{a}\right)^2$ Given $a,b,c \in \mathbb{R^+}$ such that $a+b+c=12$   Find Minimum value of $$S=\left(a+\frac{1}{b}\right)^2+\left(b+\frac{1}{c}\right)^2+\left(c+\frac{1}{a}\right)^2$$  My Try: By Cauchy Schwarz Inequality we have  $$\left(a+\frac{1}{b}\right)+\left(b+\frac{1}{c}\right)+\left(c+\frac{1}{a}\right)\le \sqrt{3}\sqrt{S}$$  $\implies$  $$\sqrt{3S} \ge 12+\frac{1}{a}+\frac{1}{b}+\frac{1}{c}$$  Now by $AM \ge HM $ inequality we have  $$\frac{a+b+c}{3} \ge \frac{3}{\frac{1}{a}+\frac{1}{b}+\frac{1}{c}}$$ $\implies$  $$\frac{1}{a}+\frac{1}{b}+\frac{1}{c} \ge \frac{3}{4}$$  hence  $$\sqrt{3S} \ge 12+\frac{3}{4}=\frac{51}{4}$$  hence  $$3S \ge \frac{2601}{16}$$  so $$S \ge \frac{867}{16}$$  is this approach correct and any better approach please share. Buster Blader the DDS did not affect Destiny Hero - Decider effect; why so? How come  with  set to dragons didn't stop 's effect from being activated? SEDE logs me out more often than it used to do I'm pretty sure that since a month or so,  seems much more eager to get rid of my session and log me out in that process. I don't mind logging in a couple of times per day, if that helps to reduce resource consumption, but the user experience isn't all that great when it happens. Here is why: I'm most often in the middle of writing a query for an MSE question, for example . So I have the edit window open and am creating a new revision of my query. When I click &quot;run,&quot; I do notice the button gets grayed-out, as it normally does, but I never get any result back. There is also no error message. To recover from this I have to copy the SQL text I have typed, open a new tab and load SEDE, log in, switch back to the stalled tab, refresh, paste the SQL text, run query. Repeat the process after 10 minutes. If the intended behavior is to log users out of their session on such short notice (I recall sessions lived for 24 hours), can there then be a slightly better handling in the browser of that state, so it is clear you're logged out once you click the run button? I prefer, however, to have the longer allowed sessions back. I'm experiencing this behavior mostly in Chrome on Win 10. I'm an Egyptian citizen, who holds Schengen visa and stay permit in Italy. Can I go to UK for some days with my stay permit and Schengen visa?