How to create ZIPs with the content of every folder
How to make 7-zip do a whole bunch of folders
Relation between rank and number of distinct eigenvalues of a matrix Let $T : V\to V$ be a linear transformation such that $\dim\operatorname{Range}(T)=k\leq n$, where $n=\dim V$. Show that $T$ can have at most $k+1$ distinct eigenvalues.   I can realize that the rank  will correspond to the number of non-zero eigenvalues (counted up to multiplicity) and the nullity will correspond to the 0 eigenvalue (counted up to multiplicity), but I cannot design an analytical proof of this.  Thanks for any help . How to fix apt: Signature by key uses weak digest algorithm (SHA1)? How do I install Ubuntu? I'm still learning, but I'm trying to follow a tutorial to apply texture to a model. I only want to apply the texture to one object in the scene, so I selected it, unwrapped it, and painted over it. Now I selected it in the Edit Mode (I can't select it in the Object mode because all is locked together) and went into Node Editor, but the nodes are greyed out.  Why? Suppress black box at end of line Under TeX, when I write a line too long, it prints a fat black box at the end of the line.  That is probably a feature, but I dislike it.  How to turn that OFF? Is there a command-line option or something else?   I usually use LaTeX, but I have a complicated file which happens to be plain TeX. What do 'real', 'user' and 'sys' mean in the output of time(1)? $ time foo real        0m0.003s user        0m0.000s sys         0m0.004s $   What do 'real', 'user' and 'sys' mean in the output of time?  Which one is meaningful when benchmarking my app? Could it be that Goldbach conjecture is undecidable? The result closest to Goldbach conjecture is Chen's theorem [Sci. Sinica 16 157–176], the proposition ``1+2''. It is natural to ask if it is likely that under our arithmetic axioms the Goldbach conjecture is an undecidable proposition. How can I require an optional Perl module if installed? I have Perl code which relies on Term::ReadKey to get the terminal width. My installation is missing this module, so I want to provide a default if the module isn't present rather than throw an exception. How can I conditionally use an optional module, without knowing ahead of time whether it is available. # but only if the module is installed and exists use Term::ReadKey; ...  How can I accomplish this? Is it possible to check out subdirectories of a repository in Git?  Imagine I am setting up a new WordPress installation. I will create two new directories for my plugin and theme customization:   wordpress/wp-content/plugins/myplugins/  wordpress/wp-content/themes/mytheme/   I want to maintain these directories via Git. In Subversion, I would accomplish this by having trunk/myplugins/ and trunk/mytheme/ directories and checking out subdirectories. Does Git have a way to accomplish the same task using a single repository?  I could just be missing the boat on some Git paradigm, as a long time SVN user with little exposure to Git.  Edit:  storing different content is an interesting way to handle this. Systemd is really slow in comparison to upstart I have been using Ubuntu for a long time now, this is what happened when I use:  Systemd: It performs really bad using systemd: it uses 95% of the CPU all the time and the PC gets really hot. Also it takes a really long time to boot (about 1.5 min, and sometimes it does not boot at all as it has a black screen at boot.)  Upstart: When I tried the upstart options at boot, it performs as expected, booted in seconds, and it was awesome as it should be.  Laptop:   AMD A8 Radeon SSD   Questions:   Why does upstart perform better than systemd? How can I debug systemd? Should I switch to upstart? If yes, how do I do it? I am currently using a macbook pro but the operating system is debian 8.2 not os x  I am using a macbook pro but there's this one device that's just draining a lot of power. This USB device: Card Reader (Apple)   32.5 W    100.0%                      Device         USB device: Card Reader (Apple)   2.60 W    100.0%                      Device         Radio device: btusb   209 mW     19.7 pkts/s                Device         Network interface: wlan0 (wl)   This device really drains my battery, I noticed that my laptop wouldn't even get 2 hours when not plugged in, I installed powertop. Made all the recommended changes but this device, I can't find out how to disable it. I don't even use that reader and forgot that it was there.  I configured all my devices to use limited power in my rc.local  echo '0' &gt; '/proc/sys/kernel/nmi_watchdog' echo 'min_power' &gt; '/sys/class/scsi_host/host0/link_power_management_policy' echo '1' &gt; '/sys/module/snd_hda_intel/parameters/power_save' echo '1500' &gt; '/proc/sys/vm/dirty_writeback_centisecs' echo 'auto' &gt; '/sys/bus/usb/devices/2-4/power/control' echo 'auto' &gt; '/sys/bus/usb/devices/1-12/power/control' echo 'auto' &gt; '/sys/bus/usb/devices/1-8.3/power/control' echo 'auto' &gt; '/sys/bus/pci/devices/0000:00:1f.3/power/control' echo 'auto' &gt; '/sys/bus/pci/devices/0000:01:00.1/power/control' echo 'auto' &gt; '/sys/bus/pci/devices/0000:00:1c.3/power/control' echo 'auto' &gt; '/sys/bus/pci/devices/0000:00:1c.4/power/control' echo 'auto' &gt; '/sys/bus/pci/devices/0000:00:1c.2/power/control' echo 'auto' &gt; '/sys/bus/pci/devices/0000:00:1c.0/power/control' echo 'auto' &gt; '/sys/bus/pci/devices/0000:00:1b.0/power/control' echo 'auto' &gt; '/sys/bus/pci/devices/0000:00:16.0/power/control' echo 'auto' &gt; '/sys/bus/pci/devices/0000:00:14.0/power/control' echo 'auto' &gt; '/sys/bus/pci/devices/0000:00:01.1/power/control' echo 'auto' &gt; '/sys/bus/pci/devices/0000:00:01.0/power/control' echo 'auto' &gt; '/sys/bus/pci/devices/0000:00:00.0/power/control' echo 'auto' &gt; '/sys/bus/pci/devices/0000:01:00.0/power/control' echo 'auto' &gt; '/sys/bus/pci/devices/0000:08:00.0/power/control' echo 'auto' &gt; '/sys/bus/pci/devices/0000:07:06.0/power/control' echo 'auto' &gt; '/sys/bus/pci/devices/0000:07:05.0/power/control' echo 'auto' &gt; '/sys/bus/pci/devices/0000:07:04.0/power/control' echo 'auto' &gt; '/sys/bus/pci/devices/0000:07:03.0/power/control' echo 'auto' &gt; '/sys/bus/pci/devices/0000:07:00.0/power/control' echo 'auto' &gt; '/sys/bus/pci/devices/0000:06:00.0/power/control' echo 'auto' &gt; '/sys/bus/pci/devices/0000:05:00.0/power/control' echo 'auto' &gt; '/sys/bus/pci/devices/0000:04:00.0/power/control' echo 'auto' &gt; '/sys/bus/pci/devices/0000:03:00.0/power/control' echo 'auto' &gt; '/sys/bus/pci/devices/0000:00:1f.0/power/control'   How can I get this device to act sanely or disable it completely because I  haven't used it. Should I vary input field lengths in a single page checkout form? I have an expression for a covariance matrix $C$ in terms of the indices $i$ and $j$.  In this way I can analytically calculate the elements of my covariance matrix, however when I try to invert $C$ matlab gives a warning about the matrix being close to singular.  The inversion therefore doesn't work, by which I mean the multiplying $C$ by the inverse given i do not get the identity.  I have tried calculating the pseudo inverse but this also does not work.  I have also tried adding a small constant along the diagonal but again the results do not work.  In general I'm working with matrices of dimension 1200 but I will give low dimensional example matrix that has the same properties, i.e. the matrices are symmetric about the diagonal and the anti-diagonal     19.9939  19.9954  19.9958  19.9951  19.9933  19.9905  19.9865    19.9954  19.9973  19.9981  19.9978  19.9965  19.9940  19.9905    19.9958  19.9981  19.9993  19.9995  19.9985  19.9965  19.9933    19.9951  19.9978  19.9995  20.0000  19.9995  19.9978  19.9951    19.9933  19.9965  19.9985  19.9995  19.9993  19.9981  19.9958    19.9905  19.9940  19.9965  19.9978  19.9981  19.9973  19.9954    19.9865  19.9905  19.9933  19.9951  19.9958  19.9954  19.9939   As mentioned in the title the matrix isn't positive, however the the negative eigenvalues are very small suggesting that the matrix is not positive only due to machine precision.  The negative eigenvalues are $-1.4048e-14$ and $-2.4571e-15$.  How can I go about inverting these matrices? How can I convert JPG into PDF easily? Why is the image of a smooth embedding $f: N \to M$ an embedded submanifold? I'm reading An Introduction to Manifolds (Tu) and got confused on p.123 Theorem 11.13. Let me briefly explain what was done before that.  The author defines an embedding between two manifolds $f: N\rightarrow M$ as an injective immersion (differential is injective everywhere) with the additional property that $f(N)$ as a subspace of $M$ is homeomorphic via $f$ to $N$. Then a canonical form theorem is proven, namely, that for any point $p \in N$, there are charts $(U,\phi = x^1, \ldots, x^n) \ni p$ and $(V,\psi = y^1, \ldots, y^m) \ni f(p)$, such that the transition map takes the following form:  $$\psi \circ f \circ \phi^{-1} : (r^1,\ldots,r^n) \mapsto (r^1,\ldots,r^n,0,\ldots,0).$$  (I guess it is implicitly assumed that $f(U) \subset V$).  Now in the process of proving that $f(N) \subset M$ is an , he states that $f(U) \subset V$ is defined by the vanishing of the coordinates $y^{n+1},\ldots,y^m$. I can prove that $$ f(U) \subset \{q \in V: y^{n+1}(q) = \cdots = y^m(q)\} $$ but not the reverse inclusion. Can anyone explain why this should be true? I think I have found the final answer $\left(4 \left[\frac{2t \cosh(4t) - \sinh(4t)}{t^2}\right]\right)$ but need to verify it. Basic Electronics Book I need basic electronics books  (diodes,transistors,current.. etc) as I am just starting out with electronics and want to have something to read over the holiday.  Any suggestions of good beginners' books? Why can't I run two mysqli queries? The second one fails How can I sort arrays and data in PHP? Is "The empty set is a subset of any set" a convention? Recently I learned that for any set A, we have $\varnothing\subset A$.  I found some explanation of why it holds.     $\varnothing\subset A$ means "for every object $x$, if $x$ belongs to the empty set, then $x$ also belongs to the set A". This is a vacuous truth, because the antecedent ($x$ belongs to the empty set) could never be true, so the conclusion always holds ($x$ also belongs to the set A). So $\varnothing\subset A$ holds.   What confused me was that, the following expression was also a vacuous truth.     For every object  $x$, if $x$ belongs to the empty set, then $x$ doesn't belong to the set A.   According to the definition of the vacuous truth, the conclusion ($x$ doesn't belong to the set A) holds, so $\varnothing\not\subset A$ would be true, too.  Which one is correct? Or is it just a convention to let $\varnothing\subset A$?