given A and B are mxn and nxm matrices. What can we say about their eigenvalues I know that the sum of the eigenvalues will be the same. But can we say something about them individually?  When A is transpose(B) I'm getting something interesting  A = (1  2  0)     (0 -1  2)  B =  (1  0)      (2 -1)      (0  2)  AB has 7,3 as eigenvalues BA has 3,7,0 as eigenvalues
Do matrices $ AB $ and $ BA $ have the same minimal and characteristic polynomials? Let $ A, B $ be two square matrices of order $n$. Do $ AB $ and $ BA $ have same minimal and characteristic polynomials?   I have a proof only if $ A$ or $ B $ is invertible. Is it true for all cases?
Cannot update grub with parameters on live USB I have booted from a live USB ("Try Ubuntu"), that also has a persistent option set (I used  to create one) to do some tests for .  I'm trying to test  (like ) by doing this  sudo nano /etc/default/grub sudo update-grub   The problem is that that last command gives me this:  /usr/sbin/grub-probe: error: failed to get canonical path of /cow.   It looks like /cow is the file-system that is mounted on /, according to:  :~# df Filesystem     1K-blocks    Used Available Use% Mounted on /cow             4056896 2840204   1007284  74% / udev             1525912       4   1525908   1% /dev tmpfs             613768     844    612924   1% /run ....   Is there a way for me to run update-grub? Prevent Photos app on OSX from launching when plugging in device I'm studying molecular biology and I'm trying to understand an experiment which shows the importance of promoters in the relative transcription level (RT). The image below comes from Rolf Knippers' book "Molekulare Genetik" (8th edition).    The legend says (among other things):     Die erste Zeile gibt die normale "Wildtyp"-Sequenz der 5'-flankierenden Region wieder.   Which, in english, means something like:     The first line repeats the normal wild-type sequence of the 5' flanking region.   The column on the right gives the relative transcription (RT) level, 1.0 being the highest possible level of transcription. As we can see, the lines where some parts of the "5' region" have been deleted give quite low RT levels, since some regions of the promoter are missing.  My questions are the following:  1) According to  and , I understand that RNA polymerase reads and uses both coding and non-coding strands in order to synthesize RNA. Therefore, how did they manage to use the sequences strands regions had been deleted to make a polymerase "read them" and perform transcription?  2) If the polymerase reads the template strand in the 3' -> 5' sense, shouldn't we talk of "ATAT box" or "TAAC box" instead of "TATA" or "CAAT" boxes? Does it mean that the "promoter" regions they are using on the graphic above are actually on the coding strand?  Thanks a lot for your help. Can the “while attuned” powers of Solarian stellar revelations be used while attuned to either mode, or only the matching one? gnome-terminal fails to start (timed out) I just upgraded from Ubuntu 16.04 to 18.04. My workflow is to connect from Windows using VcXsrv to Ubuntu (ssh with X tunneling), starting a xterm on Ubuntu. Inside the xterm I am typing gnome-terminal to get a gnome-terminal. Since the upgrade this is not working anymore. I am getting $ gnome-terminal   # Couldn't register with accessibility bus: Did not receive a reply. Possible causes include: the remote application did not send a reply, the message bus security policy blocked the reply, the reply timeout expired, or the network connection was broken.   # Error constructing proxy for org.gnome.Terminal:/org/gnome/Terminal/Factory0: Fehler beim Aufruf von StartServiceByName für org.gnome.Terminal: Zeitüberschreitung wurde erreicht    or when starting with English locale $ LANG=en_US.utf8 gnome-terminal   # Couldn't register with accessibility bus: Did not receive a reply. Possible causes include: the remote application did not send a reply, the message bus security policy blocked the reply, the reply timeout expired, or the network connection was broken.   # Error constructing proxy for org.gnome.Terminal:/org/gnome/Terminal/Factory0: Error calling StartServiceByName for org.gnome.Terminal: Timeout was reached  I am not always getting the first line, but I am always gettint the timeout error. Digging more into the issue I found out  sudo gnome-terminal works gnome-terminal works when run in a xterm when locally logged in on the PC when I am also logged in locally on the PC then gnome-terminal in the remote session's xterm opens a gnome-terminal on the local session on the PC (still getting the first error line about registering with accessibility bus) when I am also logged in over rdp (Windows network connection) then a gnome-terminal in the ssh session opens a gnome-terminal in the xrdp session when I login over rdp (Windows network connection), logoff there, then gnome-terminal can open a gnome-terminal  What can I do to get gnome-terminal in a remote session's xterm to work? My wife wants a 4th baby, but I don't My wife wants a 4th baby, but I don't.  We have been talking about it for the last few days (talking strongly).   I have raised points such as:   We will get less time to spend with our current kids. The age gap between the first and the last will be too wide. It will cost more money. She will be out of work longer. We will need a bigger house. And we don't even have our own house yet (we are still renting). We will have to start again. Sleepless nights, nappies, feeding, new cot, car seat, etc etc.   She says:   She feels like she is missing something. She has always wanted a large family. Things will be the same regardless of having 3, or 4 kids. She agrees that money will be tighter, but wants to push through it.   Our current kids are 9 months, 2 years, and 4 years. We are young married couple (25), and I have a fairly decent job.  What would be the pros and cons of having another child?   How can we rationally talk to the other about having/or not having another child?  And what should we do if we cannot agree? Find number of files with a specific extension, in all subdirectories Is there a way to find the number of files of a specific type without having to loop through all results inn a Directory.GetFiles() or similar method? I am looking for something like this:  int ComponentCount = MagicFindFileCount(@"c:\windows\system32", "*.dll");   I know that I can make a recursive function to call Directory.GetFiles , but it would be much cleaner if I could do this without all the iterating.  EDIT: If it is not possible to do this without recursing and iterating yourself, what would be the best way to do it? In all the discussions about how the heavy elements in the universe are forged in the guts of stars and especially during a star's death, I usually hear that once the star begins fusing lighter atoms to produce iron (Fe) that's the end of the star's life and the whole system collapses onto itself; and based on how massive the star was initially, it has different outcome - like a white dwarf, a neutron star or a black hole. I have rarely heard a detailed explanation of how the elements heavier than iron are produced. I would appreciate a convincing explanation of this process. Sharing Open Source Python/ArcPy Code and Models for ArcGIS Desktop? I will be writing scripts for ArcGIS Desktop in Python with ArcPy.   Is there a community or open source project where code and models can be shared? I remember reading this book in the late 80's or early 90's. It was a - sort of - semi SciFi contemporary fairy tale.  It was set in Manhattan in contemporary times, near future and (I think) late 1800's. There was a mist wall round New York that ships could disappear into and arrive out at different times.  There was a man with a white horse, the horse could fly but had forgotten how. The man is brought forward from the past but (like the horse) forgets who he is.  An engineer arrives from the future in a gigantic ocean liner and builds a bridge of light to heaven (possibly at the last millennium turn over).   It was a very involved book with a huge cast of characters that all had some part to play in the story.  In the 1800's story there was a girl suffering from consumption, she slept in a glass room on the roof of her house, open to the freezing winter air, it was what kept her alive. She was rich (the family had made money in whaling) but somehow she and The Man (the guy with the white horse, who was pretty much a nobody) met and fell in love (I think).  Some of the story was set around a lake in upstate NY, and one character started off in San Francisco (contemporary times) and traveled to the lake.  Anyone any idea what I'm talking about? What is the best practice re: API Version of your Apex Classes? I'm in the process of pushing some updates to some code I originally wrote 12-18 months ago, and the API Version is between 27.0 and 29.0  I know this is to protect the integrity of the test classes you've built (in case they have changed some things) but is there a best practice around either leaving these alone or trying to keep them up-to-date (maybe just once a year instead of at each release)? This inequality $a+b^2+c^3+d^4\ge \frac{1}{a}+\frac{1}{b^2}+\frac{1}{c^3}+\frac{1}{d^4}$ let $0&lt;a\le b\le c\le d$, and such $abcd=1$,show that   $$a+b^2+c^3+d^4\ge \dfrac{1}{a}+\dfrac{1}{b^2}+\dfrac{1}{c^3}+\dfrac{1}{d^4}$$   it seems harder than Why doesn't terminal show color schema once logged as root? I'm currently using Debian 7 Wheezy, and I've noticed that the colors palette on terminal (which might be useful to identify among a large set of files and folders) are not enabled once I log as root.  Same, I've noticed the tab completion doesn't work the same in this situation.  How can I configure these issues? Given sequence of $L-$Lipschitz functions which converges pointwise, prove uniform convergence Let $f_n:[a.b]\rightarrow \mathbb{R}$ be sequence of $L-$Lipschitz functions, that is: $$\forall x,y\in[a,b]: |f_n(x)-f_n(y)|\leq L|x-y|$$   Suppose $f_n \rightarrow f$ pointwise, prove $f_n \rightrightarrows f$   I have all the parts of the puzzle for the proof, and I'm trying to put them all together, I'm using  in my answer.  I would appreciate is you could correct my proof, and if you have an alternative proof, I would be more then happy to see it.  My proof:   Let $\epsilon&gt;0.$  $f_n$ are uniformly continuous on $[a,b]:$  $\tag{1} \exists \delta&gt;0\ \forall x,y\in[a,b]: |f_n(x)-f_n(y)|&lt;\frac{\epsilon}{3}$  $f$ is also $L-$Lipschitz:  $\tag{2} \forall x,y\in[a,b]:|f(x)-f(y)|&lt;L|x-y|=\frac{\epsilon}{3}$  Let us set a partition of $[a,b]$ such as Stephen Montgomery-Smith suggests:     Pick points $x_1,\dots,x_m \in [a,b]$ which are distance   $\frac{\epsilon}{3}$ from each other.        For each $1 \le i \le m$, find a number $N_i$ so that for all $n \ge  N_i$ we have $|f_n(x_i)-f(x_i)| \le \epsilon/3$.   Let $N = \max_{1 \le i \le m} N_i$      Now given any $x \in [a,b]$, pick $1 \le i \le m$ such that $|x-x_i| &lt;\frac{\epsilon}{3L}:  |f_n(x)-f(x)|&lt;\frac{\epsilon}{3} \tag{3}$   $$\begin{align}|f_n(y)-f(y)| &amp;=|f_n(y)-f_n(x)+f_n(x)-f(x)+f(x)-f(y)| \\ &amp;\leq |f_n(y)-f_n(x)| + |f_n(x)-f(x)|+|f(x)-f(y)| \\ &amp;&lt; \frac{\epsilon}{3} + \frac{\epsilon}{3} + \frac{\epsilon}{3} = \epsilon \\\end{align}$$ Which is correct, "you and I" or "you and me"? If $f$ is continuous and $f'(x)\ge 0$, outside of a countable set, then $f$ is increasing changed primary email in google account. how to log in? I added gmail to my google account. Now when i try to log into stack exchange using google it prompts me to create a new account instead of using the existing.   The google account is still the same but google changed the primary email adress.  How can i log in again? Fedora 14 uses vi by default when one runs visudo. Is there a way to change this to something else? I'm looking for a shapefile containing an 1000m or 2000m UTM grid ("graticule"). All I was about to find on the web is a 10000m UTM grid (here: ) and I am aware that a 1000m UTM grid for the whole world might be quite big.  That's why I'm now wondering if and how it would be possible to generate such a shapefile for a part of the world. I would prefer to use open source tools like gdal. Others output formats than a shapefile might be ok too.   Has anyone an idea? Stacking symbols