This question is from the perspective of a student who has only a fundamental idea of eigenvectors and eigenspaces (and linear algebra in general). If my understanding is correct, an eigenvector E of a vector V projects the vector V along the direction of itself by a factor of the associated eigenvalue (lambda).  Av = (lambda)v   Now, in PCA we try to find the eigenvectors of the covariance matrix of a dataset. I am unclear as to the purpose of this step: what is the practical interpretation of this? A covariance matrix cannot be interpreted as a vector, but maybe a set of vectors.
In today's pattern recognition class my professor talked about PCA, eigenvectors and eigenvalues.   I understood the mathematics of it. If I'm asked to find eigenvalues etc. I'll do it correctly like a machine. But I didn't understand it. I didn't get the purpose of it. I didn't get the feel of it.        I strongly believe in the following quote:     You do not really understand something unless you can explain it to your grandmother. -- Albert Einstein   Well, I can't explain these concepts to a layman or grandma.   Why PCA, eigenvectors &amp; eigenvalues? What was the need for these concepts? How would you explain these to a layman?
Using WFS-T in OpenLayers? How can I use WFS-T in openlayers-2?  I'm using  in server side. Setting the editing style on a UITableViewCell How does Hisoka see Gon exactly? As a rival or as a toy to entertain himself? Hisoka hinted that Gon is his treasure and also his prey, but it can't be both, right? Because in the end, he didn't want Gon to die no matter what.  So it's weird that he didn't want Gon to die but also made him his prey to fight till death. Is it sexual for Hisoka or what? I still remember the 'Schwing' thing. I have problems with getting an Asus PCE-N53 11n N600 PCI-E Adapter card to work on my desktop computer.  As far as I can tell no drivers are installed for the card. I know I can manually download the drivers directly from Asus, but I would rather not go that route.  If there are anyone that knows about any packages or other things I can do to make this work would be much appreciated.  Some systems details:  $ lsb_release -a No LSB modules are available. Distributor ID: Ubuntu Description:    Ubuntu 12.04.1 LTS Release:    12.04 Codename:   precise   $ sudo lshw -C network   *-network                       description: Ethernet interface        product: RTL8111/8168B PCI Express Gigabit Ethernet controller        vendor: Realtek Semiconductor Co., Ltd.        physical id: 0        bus info: pci@0000:03:00.0        logical name: eth0        version: 06        serial: d4:3d:7e:03:b9:1d        size: 100Mbit/s        capacity: 1Gbit/s        width: 64 bits        clock: 33MHz        capabilities: pm msi pciexpress msix vpd bus_master cap_list ethernet physical tp mii 10bt 10bt-fd 100bt 100bt-fd 1000bt 1000bt-fd autonegotiation        configuration: autonegotiation=on broadcast=yes driver=r8169 driverversion=2.3LK-NAPI duplex=full firmware=rtl8168e-3_0.0.4 03/27/12 ip=192.168.0.173 latency=0 link=yes multicast=yes port=MII speed=100Mbit/s        resources: irq:43 ioport:d000(size=256) memory:f2104000-f2104fff memory:f2100000-f2103fff  *-network UNCLAIMED        description: Network controller        product: Ralink corp.        vendor: Ralink corp.        physical id: 0        bus info: pci@0000:04:00.0        version: 00        width: 32 bits        clock: 33MHz        capabilities: pm msi pciexpress bus_master cap_list        configuration: latency=0        resources: memory:f7100000-f710ffff  $ lsmod Module                  Size  Used by nvidia              12319264  51  vesafb                 13844  1  snd_hda_codec_hdmi     32474  1  joydev                 17693  0  bnep                   18281  2  rfcomm                 47604  0  bluetooth             180104  10 bnep,rfcomm snd_hda_codec_realtek   224173  1  snd_seq_midi           13324  0  ppdev                  17113  0  snd_rawmidi            30748  1 snd_seq_midi usbhid                 47199  0  hid                    99559  1 usbhid nouveau               774641  0  parport_pc             32866  1  snd_hda_intel          33773  5  ttm                    76949  1 nouveau snd_hda_codec         127706  3 snd_hda_codec_hdmi,snd_hda_codec_realtek,snd_hda_intel drm_kms_helper         46978  1 nouveau drm                   242038  3 nouveau,ttm,drm_kms_helper snd_seq_midi_event     14899  1 snd_seq_midi snd_hwdep              13668  1 snd_hda_codec snd_seq                61896  2 snd_seq_midi,snd_seq_midi_event i2c_algo_bit           13423  1 nouveau mxm_wmi                12979  1 nouveau wmi                    19256  1 mxm_wmi mac_hid                13253  0  snd_pcm                97188  3 snd_hda_codec_hdmi,snd_hda_intel,snd_hda_codec psmouse                97362  0  video                  19596  1 nouveau snd_timer              29990  2 snd_seq,snd_pcm snd_seq_device         14540  3 snd_seq_midi,snd_rawmidi,snd_seq snd                    78855  20 snd_hda_codec_hdmi,snd_hda_codec_realtek,snd_rawmidi,snd_hda_intel,snd_hda_codec,snd_hwdep,snd_seq,snd_pcm,snd_timer,snd_seq_device serio_raw              13211  0  soundcore              15091  1 snd snd_page_alloc         18529  2 snd_hda_intel,snd_pcm mei                    41616  0  lp                     17799  0  parport                46562  3 ppdev,parport_pc,lp r8169                  62099  0 Prove $R < ( 1 + (\sum |a_{i}|^{p} )^{q/p})^{1/q}$ for absolute value of polynomial zeros Encouraging users to create an account (and keep it) I know SO's policy is &quot;you don't have to register to ask questions,&quot; but there are so many new members and so many hit-and-runs... The majority of the questions I see now are coming from new users (i.e., it's their first question). Although unregistered users should still be able to ask questions, I think we should encourage users to create an account. Here is a couple of ways we could do that:  Explicitly encourage people to get an account: there's currently nothing telling people to do that. Maybe tell people something like &quot;Get an account, it's easy!&quot; and maybe show some of the perks of having an account (and having rep).  Maybe give a few bonus points for registering; and have that enable a basic privilege. It could be taken from one of the , for example.   Of course getting people to register is just half of the battle. I don't know what the stats are on this, but I think there's a number of users who create multiple accounts anyways. We could curb that by:  Having smart(er)? duplicate account detection systems, alerting someone who is about to create a new account and possibly has an account already. Give them a message like &quot;Hey, it looks like you already have  account, are you sure you want to create a new one?&quot;  Create a new privilege (10k? 20k?) that gives users tools to detect possible duplicate accounts, eg: &quot;List users with the same e-mail,&quot; &quot;List users with the same IP addresses,&quot;  etc. (without revealing said emails and IPs). Then the 10k/20k can look at other stuff (e.g.: posts) and refer the new user to a moderator for a possible merge. Windows 10 non-persistent installation (live ISO) We've got a Windows 10 installation running in an environment where it can occasionally lose power and restart. However, this sometimes leads to corruption of files.  I've had a look at Windows "To-Go" but this seems to be persistent. And I've also checked out virtualisation, but that would require us to run a non-persistent Windows 10, in another Windows 10 environment.  Is it possible to install Windows 10 as a "non-persistent live CD"? So that a user will have a seemingly fresh Windows 10, but doesn't require to re-install it at each startup? sudo echo "something" >> /etc/privilegedFile doesn't work This is a pretty simple question, at least it seems like it should be, about sudo permissions in Linux.  There are a lot of times when I just want to append something to /etc/hosts or a similar file but end up not being able to because both &gt; and &gt;&gt; are not allowed, even with root.  Is there someway to make this work without having to su or sudo su into root? Back-transformation of regression coefficients I'm doing a linear regression with a transformed dependent variable. The following transformation was done so that the assumption of normality of residuals would hold. The untransformed dependant variable was negatively skewed, and the following transform made it close to normal:   $$Y=\sqrt{50-Y_{orig}}$$  where $Y_{orig}$ is the dependent variable on the original scale.   I think it makes sense to use some transformation on the $\beta$ coefficients to work our way back to the original scale. Using the following regression equation,   $$Y=\sqrt{50-Y_{orig}}=\alpha+\beta \cdot X$$  and by fixing $X=0$, we have   $$\alpha=\sqrt{50-Y_{orig}}=\sqrt{50-\alpha_{orig}}$$  And finally,  $$\alpha_{orig}=50-\alpha^2$$  Using the same logic, I found  $$\beta_{orig}=\alpha\space(\alpha-2\beta)+\beta^2+\alpha_{orig}-50$$  Now things work very well for a model with 1 or 2 predictors; the back-transformed coefficients resemble the original ones, only now I can trust the standard errors. The problem comes when including an interaction term, such as  $$Y=\alpha+X_1\beta_{X_1}+X_2\beta_{X_2}+X_1X_2\beta_{X_1X_2}$$  Then the back-transformation for the $\beta$s are not so close to the ones from the original scale, and I'm not sure why that happens. I'm also unsure if the formula found for back-transforming a beta coefficient is usable as is for the 3rd $\beta$ (for the interaction term). Before going into crazy algebra, I thought I'd ask for advice... Can long term sleeping at day damage your health? I've passed half or more of my life, sleeping in very late and often after the sun rises. Now I believe that I'm already feeling its effect. Some of my hormones are under the ideal levels and I have a deficiency in vitamin D.  What are the effects of sleeping during the day and not at night for work reasons or just habit? Is there any effect that can't be reversed simply by sleeping at night? (Assuming that you are sleeping enough time per day like 7-8 hours)  Could this sleep pattern be related to endocrine ills and other ills? Grep: unexpected results when searching for words in heading from man page I'm running into weird behavior when trying to grep a man page on macOS. For example, the Bash man page clearly has an occurrence of the string NAME:  $ man bash | head -5 | tail -1 NAME   And if I grep for name I do get results, but if I grep for NAME I don't:  $ man bash | grep 'NAME' $ man bash | grep NAME   I've tried other uppercase words that I know are in there, and searching for SHELL yields nothing whereas searching for BASH yields results.  What's going on here?  Update: Thanks for all the answers! I thought it worth adding the context in which I ran into this. I wanted to write a bash function to wrap man and in cases where I've tried to look up the man page for a shell builtin, jump to the relevant section of the Bash man page. There might be a better way, but here's what I've got currently:  man () {   case "$(type -t "$1")" in     builtin)       local pattern="^ *$1"        if bashdoc_match "$pattern \+[-[]"; then         command man bash | less --pattern="$pattern +[-[]"       elif bashdoc_match "$pattern\b"; then         command man bash | less --pattern="$pattern[[:&gt;:]]"       else         command man bash       fi       ;;     keyword)       command man bash | less --hilite-search --pattern='^SHELL GRAMMAR$'       ;;     *)       command man "$@"       ;;   esac }  bashdoc_match() {   command man bash | col -b | grep -l "$1" &gt; /dev/null } Prove that:  $$\displaystyle \sum_{n=m+1}^\infty \dfrac{1}{n!} \le \dfrac{1}{m\cdot m!}$$  I have tried induction on $m$ but it does not work very well. Any suggestion? So far, I didn't have the chance to use either of these services. Before starting, I would like to hear your opinions. What are the advantages and disadvantages? Why should I choose one over the other? I am mainly interested in the technical side, but I would also love to hear comments also regarding the plans and prices. How to understand the definition of vector and tensor? Physics texts like to define vector as something that transform like a vector and tensor as something that transform like a tensor, which is different from the definition in math books. I am having difficulty understanding this kind of definition. To me, it goes like this:   First we have a collection of bases or coordinate systems (do these represent reference frames?) and the transformations between them. A vector/tensor is an assignment of an array of numbers to each basis, and these arrays are related to each other by coordinate transformations.   I am wondering how coordinate systems and transformations are specified.    Do we need all possible coordinate systems and transformations to define a vector space or just a few of them? How to define the concept of basis and coordinate transformation without completing the very notion of vector? Accidentally hit "toggle full screen", How do I exit? I have installed Google Drive on Windows Server 2008 R2. When I login to the server, Google Drive starts automatically and synchrnoizes files, pulling changes down from the cloud. All good so far.  However, I would like the sync to run even if I am not logged in. Is there any way to start the sync process automatically, maybe as a scheduled task?  I have other jobs on the server which distribute the files by FTP so I would like the server copies of the files to be up to date. The following code works as expected in both Python 2.5 and 3.0:  a, b, c = (1, 2, 3)  print(a, b, c)  def test():     print(a)     print(b)     print(c)    # (A)     #c+=1       # (B) test()   However, when I uncomment line (B), I get an UnboundLocalError: 'c' not assigned at line (A). The values of a and b are printed correctly. This has me completely baffled for two reasons:   Why is there a runtime error thrown at line (A) because of a later statement on line (B)? Why are variables a and b printed as expected, while c raises an error?   The only explanation I can come up with is that a local variable c is created by the assignment c+=1, which takes precedent over the "global" variable c even before the local variable is created. Of course, it doesn't make sense for a variable to "steal" scope before it exists.  Could someone please explain this behavior? Should I use 'was' or 'were' in this example?     I was always delighted when my brother or one of my sisters was/were asked to do them. Using $g = \frac{Gm}{r^2}$, the force on a point mass located at 1 AU from the Sun ($m = 2 \cdot 10^{30} \text{ kg}$) is about ~0.006 N/kg.  Does that mean that, e.g., a 70 kg person is ~42g lighter during the day, and ~42g heavier at night? That seems like it could make a big difference for things like measuring gold bars or other weight-sensitive items. (Gold arbitrage: buy your gold during the day and sell it during the night! Risk-free profit!)  This makes me suspect that I'm overlooking something obvious, because a ~0.05% weight difference seems like something everyone would have noticed long ago. So what am I missing?    Edit: A few answers below indicate that there shouldn't be any weight difference, because the Earth orbits the Sun in free-fall. But if that's the reason, does that mean that a 1:1 tidally-locked Earth-Sun system wouldn't experience differential gravity from the Sun on opposite sides? That doesn't seem right. Alternative activity monitors for OS X? I’m a bit intrigued by the new detailed activity monitors and progress indicators in Windows 8 (copying files, the task monitor, network activity, etc.) It got me thinking: surely there must be some better alternatives to the built-in Activity Monitor.app?  “Better” as in more detailed and nicer graphs. Specifically, it would be interested and see percentage disk I/O (out of disk capacity), memory usage, and CPU usage in the same nice way   The Building windows blog has an article  in Windows 8.  I just think that OS X’s task manager — which I have always found superior — just doesn’t cut it anymore compared to what is coming in Windows 8.