Are there any interesting ways of simplifying $(\textbf{a} - \textbf{b})\times(\textbf{a}+\textbf{b})$, where $\textbf{a}$ and $\textbf{b}$ are 3D vectors before I begin to dismantle the expression into a mess like a surgeon?  Thanks in advance.   HMA
Let $\times$ = cross product and $a$ and $b$ have vector signs on them.  $a = [a_1, a_2, a_3]$  $b = [b_1, b_2, b_3]$  How would I prove this? Do I expand out cross product?  Any help is appreciated!
When should I use  or >()? I know that &lt;, &lt;(), &lt;&lt; all are used to give input and  &gt;, &gt;() which are used to redirect output.  But I don't know what is clear difference between them and when to use them.  Please explain in detail and along with references if possible. Thanks For any prime $p > 3$, why is $p^2-1$ always divisible by 24? I am trying to use a Bluetooth headset on an Ubuntu PC. I am able to connect phone to pc via BT. I can stream music to PC. But cannot hear call audio. I have checked in Android phone logs, and BT sco link is established. But when making a call or virtual call (play audio through sco path in Android phone) the audio is not audible in PC headset. SCO packets are NOT appearing in btmon logs either. Anyone successfully done this?  version- ubuntu 16.04 Installed- bluez, ofono, pulseaudio pactl sink: Name- bluez_sink.22_22_8E_DE_B9_2B,             Name: alsa_output.pci-0000_00_1b.0.iec958-stereo pactl source: Name-bluez_sink.22_22_8E_DE_B9_2B.monitor               Name: alsa_input.pci-0000_00_1b.0.analog-stereo How can I access the apache basic-auth username in a PHP script? Are battery packs allowed in hand luggage? When do merchants start paying the actual value of items without bonus effects and perks? Apparently, at one time, there was a directory of core-blocks for building Gutenberg templates on GitHub, but I'm not finding it anywhere. I talking about core/paragraph, etc.     array( 'core/paragraph', array(         'placeholder' =&gt; 'Content goes here',     ) ),     array( 'core/image', array(         ...  Thanks! How to detect Safari, Chrome, IE, Firefox and Opera browser? Query without having to specify table's schema I imported a bunch of tables from SQL Server 2000 to my 2008 database. All the imported tables are prefixed with my username eg: erpadmin.tablename.  In the table properties it lists 'erpadmin' as the db schema. When I write a query I now have to include 'erpadmin.' in front of all the table names which is confusing.  Current result:  select * from erpadmin.tablename   Desired result:  select * from  tablename How do I model the fighter's Great Weapon Fighting fighting style in Anydice? I was trying to create an AnyDice function to model the Great Weapon Fighting fighting style (which lets you reroll 1s and 2s), but I couldn't get it to work on any arbitrary dice.  I've found this one:  function: reroll R:n under N:n {    if R &lt; N { result: d12 } else {result: R} } output [reroll 1d12 under 3] named "greataxe weapon fighting"   And it works fine. But I don't know how to make the function generic so i don't need to change the d12 every time i want a different dice to reroll.  I've tried  function: reroll R:n under N:n {    if R &lt; N { result: d{1..R} } else {result: R} } output [reroll 1d12 under 3] named "greataxe weapon fighting"   but it is not giving the right probabilities. Maybe if I could fetch the die size inside the function... Help me understand Support Vector Machines I understand the basics of what a Support Vector Machines' aim is in terms of classifying an input set into several different classes, but what I don't understand is some of the nitty-gritty details. For starters, I'm a bit confused by the use of Slack Variables. What is their purpose?  I'm doing a classification problem where I've captured pressure readings from sensors I've placed on the insole of a shoe. A subject will sit, stand, and walk for a couple of minutes while pressure data is recorded. I want to train a classifier to be able to determine whether a person is sitting, standing or walking and be able to do that for any future test data. What classifier type do I need to try? What is the best way for me to train a classifier from the data I've captured? I have 1000 entries for sitting, standing and walking (3x1000=3000 total), and they all have the following feature vector form. (pressurefromsensor1, pressurefromsensor2, pressurefromsensor3, pressurefromsensor4) how to reset gnome panel? I think my gnome-panel is messed up because I alt+right click it and nothing pops up.  I'm on 12.04, classic gnome desktop.  so I used locate and found gnome-panel in .gconf somewhere, how do I clear just gnome-panel's settings so that I can add things to my panel again?   edit:  matt: ~/.gconf $ find|grep -iw panel ./desktop/ibus/panel ./desktop/ibus/panel/%gconf.xml ./apps/gnome-settings/gnome-panel ./apps/gnome-settings/gnome-panel/%gconf.xml How to really clear the terminal? I can issue the clear command or press Ctrl + L to clear the current Ubuntu terminal, but this just shifts previous output upwards and if you use mouse scroll or PgUP and PgDown keys it's hard to distinguish where the output of previous command ends and output of current command begins.  Is there a way to really clear the terminal so I won't see previous command results? The following will cause infinite recursion on the == operator overload method      Foo foo1 = null;     Foo foo2 = new Foo();     Assert.IsFalse(foo1 == foo2);      public static bool operator ==(Foo foo1, Foo foo2) {         if (foo1 == null) return foo2 == null;         return foo1.Equals(foo2);     }   How do I check for nulls? I'm trying to access an XML file within a jar file, from a separate jar that's running as a desktop application.  I can get the URL to the file I need, but when I pass that to a FileReader (as a String) I get a FileNotFoundException saying "The file name, directory name, or volume label syntax is incorrect."  As a point of reference, I have no trouble reading image resources from the same jar, passing the URL to an ImageIcon constructor.  This seems to indicate that the method I'm using to get the URL is correct.  URL url = getClass().getResource("/xxx/xxx/xxx/services.xml"); ServicesLoader jsl = new ServicesLoader( url.toString() );   Inside the ServicesLoader class I have   XMLReader xr = XMLReaderFactory.createXMLReader(); xr.setContentHandler( this ); xr.setErrorHandler( this ); xr.parse( new InputSource( new FileReader( filename )));   What's wrong with using this technique to read the XML file? Can a smaller sensor's "crop factor" be used to calculate the exact increase in depth of field? If APS-C and similar crop-sensor digital cameras have a focal length multiplying effect such that a 50mm lens has an apparent focal length closer to the field of view of an 80mm on a full frame camera, and yet at the same time the depth of field for the smaller sensor camera is more like the depth of field a 50mm lens would produce on a full frame camera (using the same aperture), then this would seem to suggest the concept of an "aperture dividing effect."  In other words, a 50mm f/1.8 lens on an APS-C camera would act more like a 80mm f/2.8 (approx. 1.8 * 1.6x) lens in 35mm equivalent — for depth of field, not considering exposure.  Can someone with a better understanding of the physics involved clarify this for me.  I've never seen this concept explicitly mentioned anywhere, so I am a bit suspect of it. How do I sort a list of dictionaries by a value of the dictionary? I have a list of dictionaries and want each item to be sorted by a specific value. Take into consideration the list: [{'name':'Homer', 'age':39}, {'name':'Bart', 'age':10}]  When sorted by name, it should become: [{'name':'Bart', 'age':10}, {'name':'Homer', 'age':39}] There a  who has no valid parent user. It is indicated that his chat account is associated to a Maths.SE account, which does not appear to exist. The user was still able to chat. Is it normal? If it's a bug, could someone look into it?  Edit: if you browse the Google cache for users named Skullpatrol, it turns out a single series of associated accounts. The user is now named . I don't know what went wrong, maybe an account merge or something like that, but it needs someone from staff looking into it with some superpowers. I also tried to update the parent user of the chat account to this &quot;Rob&quot; profile, but the interface goes all buggy on me (works for other users, fails only for this one): Reading data from a relational database into a LaTeX table I'm using Tex Live 2009 on Debian squeeze. I can upgrade if I really, really  have to, but I'd rather not. I was wondering if it would be possible to do the following.  Given some data in a (relational) database, can I extract it and automatically format it in a LaTeX table, so one would not need to manually recreate the LaTeX table if the data changes? Could one do such a thing with Lua? One would normally use a suitable language database adaptor for this, and I see Lua has . I'd like to use PostgreSQL. I'm currently using version 8.4.  Solutions not involving Lua are also fine. Just to be clear, I don't know anything about Lua and my knowledge of LaTeX programming is also extremely skimpy. I'm looking for a recipe which I can adapt if necessary. While this is not really important for my current use case, it seems like a useful general technique if possible. Understanding of the theorem that all norms are equivalent in finite dimensional vector spaces