I know how to find the orthogonal and the special linear group of $2$ by $2$ matrices. This is because I know their “defining” properties. How can I find the Lie algebra of:  $$A = \left(\begin{array}[c c]  - a_1 &amp; a_2\\    0&amp; a_1^2  \end{array}\right),$$  Where the matrices are invertible? I don’t know their defining characteristic that is my big problem. If I know it, I can use dedicated to solve. Maybe it has to do something with their matrix potential or their trace?  Please help.
I'm working on the question     Let $G$ be the group of invertible real matrices of the form $\left [\begin{array}{c c}a &amp; b\\ &amp; a^2\end{array}\right ]$. Determine the Lie algebra $L$ of $G$, and compute the bracket on $L$.   I'm familiar with how to derive the Lie algebra for a linear group like $U_n$, $SU_n$, etc. but I'm not sure what to do in a more explicit case like this.
sed fails to remove newline character It's possible to offer and award bounties of reputation on questions.   What is a bounty? How can I find questions that have a bounty attached? How do I start a bounty? When can I start a bounty? Why is the system requiring me to choose a bounty amount that's higher than the minimum? Can I use Markdown formatting in the bounty remarks? Can I edit the remark? How long is the bounty period? How do I award a bounty? Can I award a bounty to my own answer? Can I award a bounty to an old answer? If I offer a bounty on someone else's question, can I award the bounty to their answer? After awarding the bounty, can I remove it or move it to another answer at a later time? What happens if there's no answer after the bounty period? What happens if I feel my question is still unanswered? What is automatic awarding? Are bounty awards exempt from the 200 points/day reputation limit? How does Community Wiki mode affect bounties? How does user deletion or post dissociation affect bounties? Can I award a bounty to an answer from a deleted user or one where the author was dissociated? Can I offer a second bounty after the first one has expired? Can I raise my bounty? What happens if a bounty question is closed or deleted? Why can't I vote to close or migrate a bounty question? What happens if I delete my account while I have an active bounty? Do I keep an awarded bounty when I delete my answer? What happens if a question where I awarded a bounty later gets deleted or migrated? Can I cancel my bounty? Can I affect / divide / share part of my bounty to two (or more) users? How many outstanding bounties can a single user have?      See also:  in the Help Center How to delineate watersheds in QGIS? I am using qgis 2.14.17 with ubuntu16. Having as input data a DEM of the region and a river network. In the manual of qgis they suggest to use a toll of qgis: Catchment area (Parallel); I dont have this in my toolbox, anybody made the same experience and could tell me the reason for it and how to get it. It seems to offer the best solution for me.  Tools which are available are from GRASS7 and TauDEM, the latter need much more data it seems. And I am not sure if I am able to create these just out of a DEM? The GRASS7 has one tool r.water.outlet: but here one has to put the outlet coordinates, which clearly I could get out of the river network, but the idea is that they are generated by delineating the watersheds.  Somebody has an idea how to solve it?  I managed now to get SAGA run in the toolbox, nevertheless would be great if somebody could help me with the qgis tool, since it should appear?! Finding information on German soldiers from World War I and World War II? Where can I find information on German soldiers from World War I and World War II?   I am curious to find out about my ancestors' role in the wars, i.e. what rank they had, where they where fighting, with whom and anything else. I want to run Notepad++ twice. Like in this paint printscreen.  How I want it:    Not what I want:    Is this possible? Let $X_1$ and $X_2$ be independent and identically distributed exponential random variables with rate $\lambda$. Let $S_2 = X_1 + X_2$.  Q: Show that $S_2$ has PDF $f_{S_2}(x) = \lambda^2 x \text{e}^{-\lambda x},\, x\ge 0$.  Note that if events occurred according to a Poisson Process (PP) with rate $\lambda$, $S_2$ would represent the time of the 2nd event.   Alternate approaches are appreciated. The approaches provided are commonly used when learning queueing theory &amp; stochastic processes.     Recall the Exponential distribution is a special case of the Gamma distribution (with shape parameter $1$). I've learned there is a more general version of this  that can be applied. Include ALL pdf graphics in document I have several plots saved as .pdf in a folder and I would like to know if there is a way of adding all of them in a document at once, without typing the path to each file. Clothing store access in Pokémon X & Y Once the player obtains access to Lumiose City for the first time, they'll be able to visit Boutique Couture from the city's Vernal Avenue (South fork, connecting from South Boulevard). Upon entering the store without performing any other actions, the player will be turned away and informed they "aren't stylish enough" and that they should visit more places in Lumiose City before visiting again.  This description is dubious, and doesn't inform the player of what they need to accomplish to gain access. Specifically:  Even beating the game (completing the Pokémon League) fails to allow access, as does modifying the player's look, visiting most shops in all areas of Lumiose City, and performing all hair stylist, PR studio, and associated actions. Completing a set of triple battles in Restaurant Le Wow did set the event flag that allowed access in my copy of Y, but it is not clear if this is the only requirement for access.  So other players may benefit, and so I know how to repeat this process if I obtain a copy of X or the future release of Z, what exact requirements yield access to this store for the first time? I'm very new to Ubuntu, and have come to this point that I can't boot back to my Windows Vista anymore.  I thought that I would get some kind of dual boot in the beginning when booting my computer, but this doesn't seem too happen and I don't have the slightest idea on how to fix this. I was looking for help here at askubuntu, but I couldn't seem to find anything. I'm too new with this software.  I'll need hints and tips on how to fix this  Thanks for your time folks! Setting print layout to portrait using QGIS 3? Once a post has been edited, you can go into the revision list, and click "View Source".  If a post has not been edited (and I don't have the edit privilege) is there any way to see the raw Markdown?  The reason I ask I because of  - it's impossible to see the source markdown, and how it's different from the rendered Markdown.  Not exactly a huge issue, just curious! string.format format string containing { Is using only HTTPS bad in a SEO perspective? I would like to set up a new business site. I plan to direct www.example.com to example.com and only use that domain. My plan is also to only use HTTPS and not HTTP.   Does this affect the SEO for the site? E.g. do Google put lower or higher rank for sites that is only available via HTTPS? Lagrangian and Hamiltonian EOM with dissipative force I am trying to write the Lagrangian and Hamiltonian for the forced Harmonic oscillator before quantizing it to get to the quantum picture. For EOM $$m\ddot{q}+\beta\dot{q}+kq=f(t),$$ I write the Lagrangian  $$ L=\frac{1}{2}m\dot{q}^{2}-\frac{1}{2}kq^{2}+f(t)q$$ with Rayleigh dissipation function as   $$ D=\frac{1}{2}\beta\dot{q}^{2}$$ to put in Lagrangian EOM $$0 = \frac{\mathrm{d}}{\mathrm{d}t} \left ( \frac {\partial L}{\partial \dot{q}_j} \right ) - \frac {\partial L}{\partial q_j} + \frac {\partial D}{\partial \dot{q}_j}. $$  On Legendre transform of $L$, I get $$H=\frac{1}{2m}{p}^{2}+\frac{1}{2}kq^{2}-f(t)q.$$  How do I include the dissipative term to get the correct EOM from the Hamiltonian's EOM? How to enable top bar background opacity? There is a way to change top bar background opacity in ubuntu 20.04 lts.  I installed the hide top bar extension but is not a option to change it. Why are moderators now required to report underage users? Just today (December 2, 2020), a  was enacted, which requires moderators to report users that they find to be underage:  If you find a user claiming to be under 16 escalate it to us through the &quot;Contact Community Team&quot; button and select the &quot;underage user&quot; template - this will flag the on-duty CM for action so we can investigate and, if deemed necessary, delete that account and all personal data associated with it. [...] This policy only applies to sites where you are a moderator. If you see things on a site where you’re not, there is no obligation to escalate.  Being part of the , moderators are required to follow the instructions there, and not following them is considered a violation of the moderator agreement. However, this contradicts a , which states (bold added):  Users and moderators are not legally responsible for underage users and are under no obligation to report them to us. If out of concern you would like to report it, [...]  As part of the re-enaction of the policy on December 2, the text &quot;and moderators&quot; in the above quote was edited out of that statement. Why are moderators now required as per policy to report underage users that they come across? Is there a legal explanation as to why SE's stance on this changed? I'm aware of  from a then-employee, which stated that moderators are expected, but not required as a condition of remaining a moderator, to report underage users. However, the new policy requires reporting them. Why? An example of a case where a moderator may not want to report an underage user is if the user claims to be from an EU country that has reduced the required age from 16. While SE's Terms of Use specify a blanket limit of 16 to comply with regulations in all EU countries, individual member states do have the ability to reduce the limit, so long as it's not below 13. There is no law violation if, say, a 15-year-old user from an EU country that has reduced the age limit to 14 registers, so a moderator may not feel like reporting them (since in that case they're merely enforcing the Terms of Use, which they're not otherwise expected to do).  The policy was recanted a few days after it was originally enacted on October 15, 2020, but was enacted again on December 2 after minor revisions following a review among moderators. The same question still applies to the revised policy, however. Removing all 'stable' theme's CSS from a Drupal 8 custom theme I would like to remove all CSSs automatically included from stable theme:  /core/themes/stable/css/system/components/*   I can remove them one by one inside the .info.yml file:  stylesheets-remove:   - 'core/themes/stable/css/system/components/ajax-progress.module.css'   - 'core/themes/stable/css/system/components/autocomplete-loading.module.css'   - ...   Is there a way to remove all of them at once?   Something like:  stylesheets-remove:   - 'core/themes/stable/css/system/components/*' Story about building up speed leading to increased quality of life Suppose $f,g$: $\Bbb R$ → $\Bbb R$ are continuous functions such that $f(r) = g(r)$ for all $r$ in $\Bbb Q$. That is to say, $f$ and $g$ are equal on the rational numbers.   Prove that  $f(x) = g(x)$  for all $x$ in $\Bbb R$ Going through the spells, I see the phrase "Willing creature" used to determine who you can cast some spells on. I don't ever see a proper definition of what a willing creature is, but I would assume that it would go something like if you asked them "Can I perform this spell on you" they would answer yes. Is there a more formal definition of what makes a target willing in 5e?  What are the ways I could make an otherwise unwilling creature willing? Suggestion spells, for instance, should probably work but what other options do I have?