Proving inverse of transpose is transpose of inverse
Transpose of inverse vs inverse of transpose
Is it possible to extend a tourist Schengen visa (12 more days)? My daughter applied at the Italian Consulate in Philadelphia, and they gave her two entries for 20 days (we thought it was for 20 days each entry). She was in Italy 12 days, then went to England for 1 week and flew to Venice to take a 10-day cruise. She couldn't make it because they said she has only 8 remaining days, but she still has a land tour already paid this week.  What can she do? Can she extend the Schengen visa for 12 more days? Right now, she is in Madrid, but next week she has to fly from Barcelona to Paris to start with the tour. What would happen if she decides to take the tour with the expired visa? She is a US permanent resident. Can Objective C determine the caller object reference at runtime (reflection)? Prove that $J^+AJ$ has positive eigenvalues Let $J \in \mathbb{R}$ be a $m \times n$ matrix of rank $n$ and a $A \in \mathbb{R}$ be a $m \times m$ diagonal positive definite matrix. Denote by $J^+$ a  of $J$.   As was shown  $J^+AJ$ is not positive definite in general.   However, I was wondering whether one can prove or disprove that $J^+AJ$ has real and positive eigenvalues. How to create animated GIF images of a screencast? I've seen animated GIF images of screen casts (like the one below) promoted a few times on this site as a way to improve answers.    What toolchain is being used to create these? Is there a program that does this automagically, or are people taking screencasts, converting them into a series of static frames, and then creating the GIF images? Editing default custom object home screen I would like to add a custom button (URL to Flow) to my default home page for my custom object. Currently, I have a default "New" button to create a new record (see attached screen shot). I'm wanting to add my Flow custom button to this page. Is there a way to do this?  Cheers, Sean. How to get the CPU cycle count in x86_64 from C++? What does "Could not find or load main class" mean? so i change my MAC address with macchanger -A wlp68s0b1 at boot with crontab, here is what happens when i disconnect and reconnect :  while connecting after boot :  rahman@debian:~$ macchanger -s wlp68s0b1 Current MAC:   00:22:31:c6:38:45 (SMT&amp;C Co., Ltd.) Permanent MAC: 00:00:00:00:00:00 (FAKE CORPORATION)   after disconnecting :  rahman@debian:~$ macchanger -s wlp68s0b1 Current MAC:   16:7b:e7:3c:d3:cd (unknown) Permanent MAC: 00:00:00:00:00:00 (FAKE CORPORATION)   after reconnecting :  rahman@debian:~$ macchanger -s wlp68s0b1 Current MAC:   00:00:00:00:00:00 (FAKE CORPORATION) Permanent MAC: 00:00:00:00:00:00 (FAKE CORPORATION)   and so on, and with every disconnect i get a different random MAC address which fades on reconnecting giving me my real MAC address , what causes that and how to stop it ?  some outputs :  rahman@debian:~$ lspci -nn |grep 14e4 44:00.0 Network controller [0280]: Broadcom Limited BCM4313 802.11bgn Wireless Network Adapter [14e4:4727] (rev 01) rahman@debian:~$ uname -a Linux debian 4.9.0-3-amd64 #1 SMP Debian 4.9.30-2+deb9u5 (2017-09-19) x86_64 GNU/Linux rahman@debian:~$ sudo ifconfig  enp0s25: flags=4099&lt;UP,BROADCAST,MULTICAST&gt;  mtu 1500         ether 00:24:c0:7b:a8:8b  txqueuelen 1000  (Ethernet)         RX packets 0  bytes 0 (0.0 B)         RX errors 0  dropped 0  overruns 0  frame 0         TX packets 0  bytes 0 (0.0 B)         TX errors 0  dropped 0 overruns 0  carrier 0  collisions 0         device interrupt 20  memory 0xd4800000-d4820000    enp0s25:avahi: flags=4099&lt;UP,BROADCAST,MULTICAST&gt;  mtu 1500         inet 169.254.9.109  netmask 255.255.0.0  broadcast 169.254.255.255         ether 00:24:c0:7b:a8:8b  txqueuelen 1000  (Ethernet)         device interrupt 20  memory 0xd4800000-d4820000    lo: flags=73&lt;UP,LOOPBACK,RUNNING&gt;  mtu 65536         inet 127.0.0.1  netmask 255.0.0.0         inet6 ::1  prefixlen 128  scopeid 0x10&lt;host&gt;         loop  txqueuelen 1  (Local Loopback)         RX packets 9436  bytes 6584515 (6.2 MiB)         RX errors 0  dropped 0  overruns 0  frame 0         TX packets 9436  bytes 6584515 (6.2 MiB)         TX errors 0  dropped 0 overruns 0  carrier 0  collisions 0  wlp68s0b1: flags=4163&lt;UP,BROADCAST,RUNNING,MULTICAST&gt;  mtu 1500         inet 192.168.1.5  netmask 255.255.255.0  broadcast 192.168.1.255         inet6 fe80::6711:9875:eb78:24fc  prefixlen 64  scopeid 0x20&lt;link&gt;         inet6 fd9c:c172:b03b:ce00:f1e0:695e:7da0:91a  prefixlen 64  scopeid 0x0&lt;global&gt;         ether 00:00:00:00:00:00  txqueuelen 1000  (Ethernet)         RX packets 484346  bytes 641850809 (612.1 MiB)         RX errors 0  dropped 0  overruns 0  frame 0         TX packets 368394  bytes 44259668 (42.2 MiB)         TX errors 0  dropped 0 overruns 0  carrier 0  collisions 0  rahman@debian:~$ sudo iwconfig  lo        no wireless extensions.  enp0s25   no wireless extensions.  wlp68s0b1  IEEE 802.11  ESSID:"3bdo"             Mode:Managed  Frequency:2.447 GHz  Access Point: 9C:C1:72:B0:3B:D4              Bit Rate=65 Mb/s   Tx-Power=30 dBm              Retry short limit:7   RTS thr:off   Fragment thr:off           Encryption key:off           Power Management:off           Link Quality=54/70  Signal level=-56 dBm             Rx invalid nwid:0  Rx invalid crypt:0  Rx invalid frag:0           Tx excessive retries:4  Invalid misc:183   Missed beacon:0 UMVUE of $e^{-\lambda}$ from poisson distribution Let $X_1,\ldots,X_n \sim$ Poisson$(\lambda)$. I wish to find UMVUE of $e^{-\lambda}$. Here $\overline{X}_n$ is complete and sufficient for $\lambda$ (hence for $e^{-\lambda}$??). Define $Y_i=1$ if $X_i=0,$ $Y_i=0$ otherwise. Clearly (I checked!) each $Y_i$ and hence $\overline{Y}_n$ is unbiased for $e^{-\lambda}$. Then I should be able to use the Lehmann Scheffe theorem to deduce the UMVUE. The estimator I get looks like $$\frac{1}{n} E\left\{\#X_i:X_i=0 \mid \sum_{i=1}^n X_i\right\}$$ whereas the correct answer is $$\left(\frac{n-1}{n}\right)^{\sum_{i=1}^n X_i}$$ I'd appreciate if anyone lets me know where I'm going wrong and guides me into the right path. Thank you. Suppose that $f$ is holomorphic on $\mathbb C$ and that $\Re(f(z))\ge 0$ for all $z$. Show that $f$ is constant. [Hint: consider $e^{−f(z)}$.]   My thoughts: If $\Re(f(z))\ge 0 $ holds, then $e^{−f(z)}$ is a bounded holomorphic function (do I need to prove this or is it obvious?) So then by Liouville's Theorem $e^{−f(z)}$ is constant.   But then I'm not sure how to rigorously go from this $\exp(−f(z))$ back to $f(z)$.   Could anyone help me piece this together please?  Thanks What does A a() mean? accounting for LED resistance Prove that for every $n\geq m \geq1$ natural numbers, the following number is an integer:  $${\gcd(n,m)\over n}\cdot{n\choose m}$$  Where $\gcd$ is the greatest common divisor.  I tried to make it simpler by cancelling the $n$ from the left side, and making it $(n-1)!$ on the right: $\gcd(n, m) \cdot \frac{(n-1)!}{m!(n-m)!}$, but can't really go further.   This was problem B-2 on the . Do particles in a sound wave ever move transversally? I'm trying to visualize how sound waves work and I was curious about something.   So sound moves in longitudinal waves, which I think I understand.  There is a really good  explaining this.  In the video the air particles are depicted as moving from left to right (longitudinally). But do they ever move up and down even a little bit? Are they on some kind of fixed axis where they can only move longitudinally and never move even the slightest bit in a vertical direction? Find duplicate records in MySQL N circles in the plane Challenges with Key with Gaps? How to revert an update? The latest xorg update was a big regression for me on a dual display setup. Is there a simple way to revert to the previous version?  I'm on Lucid Lynx. Calculate integral $\int_{-1}^{1} (1-x^2)^n dx $ Did other meta-humans enter a coma? In the first episode of The Flash (2014), Barry's struck by lightning, some chemicals fall on him, and he enters a coma for 9 months.  This happens when the S.T.A.R. Labs particle accelerator is turned on for the first time.  9 months later, he wakes up and has powers.  He then starts fighting crime, especially other meta-humans who were created by the same particle accelerator accident.  However, this is all 9 months after the accident, where were the other meta-humans during those 9 months?  The S.T.A.R. Labs people make it sound like they hadn't seen any meta-humans active during the 9 months Barry was out.  Did all people granted powers by the particle accelerator accident also fall into comas?  Why weren't they active heroes/villains during the 9 month gap?