When $AB=BA$, form of $A$
A linear operator commuting with all such operators is a scalar multiple of the identity.
I am logging in to my Ubuntu Server using my username. Once I am logged in I am typing passwd command. Entering a new password but a second after getting following error messages:  passwd: Authentication token manipulation error passwd: password unchanged   What is wrong here? How can I change my password otherwise if I don't have access to that server physically, i.e. I am connecting remotely with ssh using terminal. What is the best way to modify a list in a 'foreach' loop? I'm going to accessing my ubuntu machine remotely from my windows machine through putty. Are there any suggestions for possible ways to get an X server running on my windows machine?  Thanks. I want to make an arena where mobs will fight each other and a player can bet on one side or the other. For example: There are 2 skeletons in dyed armor; red and blue. Each color representing a team. When they spawn I want them to fight each and then when one dies I want it to announce which team is the winner and give the player the "money" due. I'm just not sure how to get the skeletons to attack each other without a player instigating it. Adding dynamic graphics to an animation How can I remove gpg key that I added using apt-key add -? I don't need the key in my server's keyring anymore. Is it possible to remove it? I added the key using this command:   curl http://repo.varnish-cache.org/debian/GPG-key.txt | apt-key add -   Thanks for helping Java Object Reuse Should Java Objects be reused as often as it can be reused ? Or should we reuse it only when they are "heavyweight", ie have OS resources associated with it ?  All old articles on the internet talk about object reuse and object pooling as much as possible, but I have read recent articles that say new Object() is highly optimized now ( 10 instructions ) and Object reuse is not as big a deal as it used to be.  What is the current best practice and how are you people doing it ? Can I travel domestically within the United States with my USA expired passport? I need to fly domestically within the United States. The only ID I have is an expired USA passport.  Can I use that to pass T.S.A.?  Can I use it as ID? The startup disk cannot be partitioned or restored to a single partition. Windows 10 and Mojave The startup disk cannot be partitioned or restored to a single   partition.      The startup disk must be formatted as a single Mac OS Extended   (Journaled) volume or already partitioned by Boot Camp Assistant for   installing Windows.   I had installed Windows 10 via bootcamp in my mac. Current version is 10.14.1  Now I don't want windows and need that space back but getting above error when I go bootcamp to remove it.  This is the output of diskutil list  /dev/disk0 (internal, physical):    #:                       TYPE NAME                    SIZE       IDENTIFIER    0:      GUID_partition_scheme                        *251.0 GB   disk0    1:                        EFI EFI                     209.7 MB   disk0s1    2:                 Apple_APFS Container disk1         181.3 GB   disk0s2    3:       Microsoft Basic Data BOOTCAMP                60.3 GB    disk0s3    4:           Windows Recovery                         509.6 MB   disk0s4  /dev/disk1 (synthesized):    #:                       TYPE NAME                    SIZE       IDENTIFIER    0:      APFS Container Scheme -                      +181.3 GB   disk1                                  Physical Store disk0s2    1:                APFS Volume Macintosh HD            116.4 GB   disk1s1    2:                APFS Volume Preboot                 44.6 MB    disk1s2    3:                APFS Volume Recovery                512.8 MB   disk1s3    4:                APFS Volume VM                      4.3 GB     disk1s4   And this is of diskutil cs list  No CoreStorage logical volume groups found   Can anybody please help me to solve this problem?  Output after I tried commands given in the first answer  ❯ diskutil list /dev/disk0 (internal, physical):    #:                       TYPE NAME                    SIZE       IDENTIFIER    0:      GUID_partition_scheme                        *251.0 GB   disk0    1:                        EFI EFI                     209.7 MB   disk0s1    2:                 Apple_APFS Container disk1         250.8 GB   disk0s2  /dev/disk1 (synthesized):    #:                       TYPE NAME                    SIZE       IDENTIFIER    0:      APFS Container Scheme -                      +250.8 GB   disk1                                  Physical Store disk0s2    1:                APFS Volume Macintosh HD            116.4 GB   disk1s1    2:                APFS Volume Preboot                 44.6 MB    disk1s2    3:                APFS Volume Recovery                512.8 MB   disk1s3    4:                APFS Volume VM                      3.2 GB     disk1s4 Self-promotion in chat We know from the  that it is accepted only in a limited way in answers and frowned upon if found to be spammy. We know from  that it can be deleted at any time from comments if the comment is not relevant or spammy.  But what about the chat? This leaves chat to be the only legitimate place to promote products or services that the user is affiliated to (albeit in an ad-like way).  What is your opinion? Why do mirrorless cameras have quicker autofocus than SLRs using live view? What test can I use to compare slopes from two or more regression models? I would like to test the difference in response of two variables to one predictor. Here is a minimal reproducible example.   library(nlme)  ## gls is used in the application; lm would suffice for this example m.set &lt;- gls(Sepal.Length ~ Petal.Width, data = iris,                 subset = Species == "setosa") m.vir &lt;- gls(Sepal.Length ~ Petal.Width, data = iris,                 subset = Species == "virginica") m.ver &lt;- gls(Sepal.Length ~ Petal.Width, data = iris,                 subset = Species == "versicolor")   I can see that the slope coefficients are different:  m.set$coefficients (Intercept) Petal.Width    4.7771775   0.9301727 m.vir$coefficients (Intercept) Petal.Width    5.2694172   0.6508306  m.ver$coefficients (Intercept) Petal.Width     4.044640    1.426365    I have three questions:   How can I test the difference between slopes? How can I test the difference between residual variances? What is a simple, effective way to present these comparisons?    A related question, , suggests re-running the model with a dummy variable to differentiate the slopes, are there options that would allow the use of independent data sets? How to transit through Delhi without a visa? What are sentences like "the longer X, the more Y" called and can they be used in formal written English? What is the type of sentence exemplified below called? Is it appropriate to use it in a scientific paper and formal written English in general?     1. The more pronounced the variation, the   more the waste.      2. The more you give, the more you get.      3. The longer I live, the more I realize the impact of attitude on life. From A Classical Introduction to Modern Number Theory by Ireland and Rosen, page 33:     Corollary 1 (Euler's Theorem). If $(a,m) = 1$, then $a^{\phi(m)} \equiv 1\,(m)$.      Proof. The units in $\mathbb{Z}/m\mathbb{Z}$ form a group of order $\phi(m)$. If $(a,m) = 1$, $\bar{a}$ is a unit. Thus $\bar{a}^{\phi(m)} = \bar{1}$ or $a^{\phi(m)} \equiv 1\,(m)$.   If I'm interpreting this correctly, this proof implicitly uses the fact(?) that if $G$ is a group and $x\in G$, then $x^{|G|}=1$, where $1$ is the identity element of $G$.  If this is indeed true, can someone explain why? (I have had no prior exposure to group theory.) Add air resistance to projectile motion I am given an initial x and y position and initial velocity and I was asked to graph the trajectory in 1 second intervals.  This is what I have so far:  If $x_0 = 1, v_{0x} = 70, y_0 = 0, v_{0y} = 80, a_x = 0, a_y = -9.8$, and time will be 0,1,2,3... and so on.  Using these equations on every second you can find the plot will be a bell shaped with the highest point being ~ 325 m at about 600 seconds:   $$ x = x0 + (v_{0x})t + 1/2((a_x)t^2) $$ $$ y = y0 + (v_{0y})t + 1/2((a_y)t^2) $$  Usually in physics, we are taught in perfect condition with no air resistance. But what if there was air resistance? How would it affect this problem? How can i add it to my calculations and see what the difference is? Why do archery arrows tilt downwards in their descent? How do I test a nonlinear association? For plot 1, I can test the association between x and y by doing a simple correlation.   For plot 2, where the relationship is nonlinear yet there is a clear relation between x and y, how can I test the association and label its nature? Is it possible to combine processing power of 2 computers? Wolfram alpha says there are no solutions. Is this because of the following?  $$\tan(z)=i \Rightarrow \frac{e^{iz}-e^{-iz}}{i(e^{iz}+e^{-iz})}=i \Rightarrow \frac{e^{iz}-e^{-iz}}{(e^{iz}+e^{-iz})}=-1$$ Let $x=e^{iz}$. Then,  $$\frac{x-1/x}{x+1/x}=-1 \Rightarrow x-1/x=-x-1/x \Rightarrow 2x=0$$  Then, $$x=e^{iz} \Rightarrow \ln(0)=iz$$ but $\ln(0)$ does not exist so we have no solutions?