What's the easiest/fastest way of calculating the determinant of $$\begin{pmatrix}a &amp; b &amp; c &amp; d\\ -b &amp; a &amp; -d &amp; c\\ -c &amp; d &amp; a &amp; -b \\ -d &amp; -c &amp; b &amp; a\end{pmatrix}$$? The result is $(a^2+b^2+c^2+d^2)^2$. This determinant occurs in Zarhin's trick (if $A$ is an Abelian variety, $(A \times A^t)^4$ is principally polarised).
I need to calculate the following determinant in order to prove the following equality:  $$\det\begin{pmatrix} a &amp; b &amp; c &amp; d \\ -b &amp; a &amp; -d &amp; c \\ -c &amp; d &amp; a &amp; -b \\ -d &amp; -c &amp; b &amp; a \end{pmatrix} = (a^2+b^2+c^2+d^2)^2.$$  I tried using Gauss-algorithm to get an easier matrix, but I'm not sure if I did it correctly.  Calling the $4$ lines $I$, $II$, $III$ and $IV$, I did:  (1) $II \cdot a$  (2) $III \cdot a$  (3) $IV \cdot a$  After this I did:  (4) $II' + I \cdot b$  (5) $III' + I \cdot c$  (6) $IV' + I \cdot d$  So finally I got the following matrix:  $$\begin{pmatrix} a &amp; b &amp; c &amp; d \\ 0 &amp; a^2+b^2 &amp; bc-ad &amp; ac+bd \\ 0 &amp; ad+bc &amp; a^2+c^2 &amp; cd-ab \\ 0 &amp; bd-ac &amp; ab-cd &amp; a^2+d^2 \end{pmatrix}.$$  I thought this would make the determinant a bit easier, unfortunately I must have done something wrong. Is multiplication with single lines allowed as I have done it?  Thank you very much.
Practical way to implement prevention of IP Spoofing I am an undergraduate Computer Science student and was hoping to gain some knowledge of ways to help prevent IP spoofing but all the resources I have tried out elaborate this concept in a theoretical way. I want to try out my hands at one of the techniques like:      How do I simulate this whole situation in my own system were I myself am the attacker and I myself have to defend it? And once I have gained an understanding of it, then how do I start translating that into programming terms? I want to run a ppp connection when my USB modem is connected, so I use this udev rule:  ACTION=="add", SUBSYSTEM=="tty", ATTRS{idVendor}=="16d8",\     RUN+="/usr/local/bin/newPPP.sh $env{DEVNAME}"  (My modem appears in /dev as ttyACM0)  newPPP.sh:  #!/bin/bash /usr/bin/pon prov $1 &gt;/dev/null 2&gt;&amp;1 &amp;   Problem:  The udev event fires, and newPPP.sh is running, but newPPP.sh process is killed after ~4-5s. ppp does not have time to connect (its timeout is 10s for dial up).  How can I run a long time process, that will not be killed?  I tried using nohup, but it didn't work either.  System: Arch Linux  Update  I found a solution , thanks to .  I use at now to run my job detached from udev process.  But the one question remains unanswered: Why do nohup and &amp; not work? I'm currently an M. Phil student in Math and I failed a course last semester because I was not able to hand in a home work assignment (which was worth 40% of my grade) on time (I was 30 minutes late).   Apart from that I'd say I'm a fairly decent student, I got an upper second class honours bachelors degree, I have a B+ and A's for all my other courses in my current programme and I'm almost finished with my first paper to be published.   I've however been deeply worried about this failure as it would reflect poorly on my transcript if I were to apply to a Ph.D or another Master's programme.   Will my failing grade affect my chances of getting into a competitive programme or greatly lower my chances of getting a scholarship? which analysis fit the best for the data? I am trying to work on the data of my master thesis. I have to create a model, but I don't know which analysis perform. My data look like this     number ID sp ab alt SWdiv     1 A1 4 6 630 0.25802965   2 A2 9 16 750 0.29235324   3 A3 8 14 850 0.411620203   4 A4 9 22 950 0.444079553   5 A5 2 12 1050 0.294855765   6 A6 13 40 1130 0.298451014   7 B1 2 2 750 0.275329152   8 B2 5 6 850 0.043352118   9 B3 14 16 950 0   10 B4 17 58 1050 0.230358688   11 B5 7 9 1150 0.298759725   12 B6 8 68 1250 0.012192474   13 C1 12 20 830 0.467542842   14 C2 13 19 930 0.454480722   15 C3 6 30 1030 0.464584038   16 C4 7 14 1130 0.448191833   17 C5 5 15 1250 0.052045275   18 C6 2 7 1315 0.051767368   19 D1 3 3 650 0.294855541   20 D2 11 17 750 0.291717599   21 D3 9 46 850 0.084284864   22 D4 8 57 950 0.088574421   23 D5 4 32 1050 0.160873283   24 D6 13 22 1150 0.297638962   25 D7 6 22 1250 0.290733158   26 E1 11 23 800 0.250878932   27 E2 8 8 900 0.418021272   28 E3 10 13 1000 0.132159303   29 E4 5 10 1100 0.058487554   30 E5 5 15 1200 0.250310822   31 E6 10 19 1350 0.01600807   32 F1 6 20 800 0.462497319   33 F2 15 54 900 0.376552904   34 F3 6 13 1000 0.298264791   35 F4 6 13 1100 0.394736812   36 G1 14 22 830 0.391455956   37 G2 11 16 930 0.282922551   38 G3 5 10 1030 0.282398234   39 G4 10 15 1130 0.153502726   40 G5 13 18 1230 0.051586706   41 H1 10 11 700 0.3009609   42 H2 7 14 800 0.579228102   43 H3 5 11 900 0.528108703   44 H4 20 48 1000 0.28689587   45 H5 13 18 1100 0.264542772   46 H6 10 20 1250 0.29928462   47 I1 12 13 535 0.35326876   48 I2 3 5 635 0.273947657   49 I3 18 30 720 0.467208221   50 I4 16 188 835 0.276669711   51 I5 7 69 935 0.000867067   52 L1 6 10 435 0.36910895   53 L2 7 20 606 0.236700524   54 L3 14 33 697 0.111132519   55 L4 17 42 797 0.296757045   56 L5 5 7 910 0.27539552   57 L6 10 15 1000 0.29748451   58 L7 6 11 1101 0.276755556     58 sample points each has two value: altitude and diversity index related to habitat heterogeneity. 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