I am trying to derive ELM going through the basics , please help me out here :   $$f = x^Tx$$ $$g = Ax-b $$   The constraint is $Ax-b = 0$  I calculated $J' = f'+\lambda^T g'$ which is $2x+(\lambda^T A)^T = 0 $ and $Ax-b=0$ . I dont know what to do next please help me out .
How can you prove that the normal equations: $(X^TX)\beta = X^TY$ have one or more solutions without the assumption that X is invertible?  My only guess is that it has something to do with generalized inverse, but I am totally lost.
The orbit of satellites around Earth eventually decays, or so I read. This is typically caused either by atmospheric drag, or by tides. I would assume most satellites have a limited service life in orbit. Hence the question - What is the typical orbital life of a satellite? How long before it's successor must be launched into orbit ?  EDIT: For instance, a weather satellite The novel centers around a man living a comfortable existence in the pretty distant future.  To support himself, he is occasionally asked to enter a box which will copy his entire body, and send it out faster than the speed of light to some developing world, to work.  His copy on this world wakes up and realizes what a big mistake he's made.  The copy does grueling work, feels lonely, and eventually just dies of radiation sickness.  Back on earth, the man never realizes how bad it is out there, and keeps sending out more copies.  I think the story is probably 80s or earlier - not sure if it's a short story, or the beginning of a novel which I lost &amp; never finished. What do you call someone who can't keep secrets? Some one who is not good at keeping secrets. In my native language it is called "chugalkhor" but it's a slang. So I can't translate it.  What do you call such a person who can't keep secrets because his instincts don't let him. How do I check if an element is hidden in jQuery? How do I counter-knife an enemy? When you press down the right stick to counter the attack, do you just press it, repeatedly press it, or press and hold? I've been knifed a few times from the front and each time I try to counter I fail. Also, if you believe you are about to be knifed and hold down the right stick until you are knifed, will that counter an attack, or do you have to press it down just at the right time? How can I initialise a static Map? How would you initialise a static Map in Java?  Method one: static initialiser  Method two: instance initialiser (anonymous subclass) or some other method?  What are the pros and cons of each?  Here is an example illustrating the two methods:  import java.util.HashMap; import java.util.Map;  public class Test {     private static final Map&lt;Integer, String&gt; myMap = new HashMap&lt;&gt;();     static {         myMap.put(1, "one");         myMap.put(2, "two");     }      private static final Map&lt;Integer, String&gt; myMap2 = new HashMap&lt;&gt;(){         {             put(1, "one");             put(2, "two");         }     }; } In Catan, can you continue a "circular" road? If I have 6 roads that go all around a single hex tile, they are a continuous uninterrupted road (assuming none of my opponents interrupts it with their settlements/cities). But, can I continue this 6-piece road and create a 7-piece continuous road by building a road that goes out of this hex tile? Here's an image of what I'm talking about:    Is this a valid 7-piece continuous road? How do I remove a file named "NUL" on Windows? I have a Windows XP box (NTFS filesystem) on which I found a file named NUL. I have not been able to remove this file in any usual way. The file appears to be owned by Administrator in the SYSTEM group, unlike any other file in the same directory (the other files are owned by my user id).  How do I get rid of this file? Where did it come from? This question is related to "The Last Jedi":  The maneuvre that vice admiral Holdo (with the purple hair) uses towards the end of the film seems remarkably effective.   It seems that it would have worked pretty well much earlier. Especially as two other ships were just allowed to run out of fuel and be destroyed.  It seems doing it earlier with different assets would have incurred less losses. Yet nobody seemed to consider it. Any in universe reason why? I am trying to prove the following.  Proposition Let $g$ be a Lie algebra such that the first derived algebra $Dg$ is a proper ideal of $g$. Consider the quotient $g/D^1 g$, and show that the preimage of any codimension 1 subspace is   an ideal, and has codimension 1.   I could show that the preimage is indeed an ideal, but I need some help with the part about the dimensions:  So suppose that $\phi: x \mapsto [x]$ is the quotient projection. And write $[h] + Dg$  for a codimension 1 subspace of $g$ (here $h\subset g$). Then the preimage of this subspace is just the linear span $h+Dg\leq g$. Let $y+z \in h+Dg$ with $y\in h$ and $z\in Dg$. Let $x\in g$. We want to show that $[x, y+z]\in h$, ie that $h + Dg \lhd g$. We can write $x$ as $x_0+x_1$ for $x_0 \in Dg$, $x_1\not\in Dg$. Then  $$[x,y+z] = [x_0, y+z] + [x_1, y] + [x_1,z] \in h + Dg$$  The inclusion follows since $Dg$ is an ideal so the first and third terms belong $Dg$; and $[x_1, y] \in D_g$, as $g/Dg$ is abelian. How to effectively use the man pages? I am looking forward to mastering linux. I have been repeatedly told to refer to man pages when you are in doubt.   Though I am very comfortable with the commandline, I find it very difficult to quickly and efficiently use man to find help with commands. Hence I end up googling up how to get things done. It is even more painful when the system I am using does not have internet access and I have to walk back to my office to get help from the internet.  How does one master man pages? What are the most common tricks that can be used to quickly get whatever you want from the man page? What are the most commonly used keyboard shortcuts? Meaning of convolution? how to copy or backup files ignoring dot files I want to back-up all files from my laptop partitions to external HDD.  I ran, for example  cp -a /med*/ravb*/*00   /med*/ravb*/M*L*/7.3GB_CP &amp;&amp; echo "7.3GB BACKED UP PROPERLY" || echo "7.3GB FAILED TO BACK UP"   The issue is that dot files are also getting included which I don't want. What should I do so as to ignore all dot files for backing up. I have a 250G disk on my Mac with around 100G in use. But the system reports only around 20G of free space. I'm using macOS 10.13.2. I have the problem at least since the upgrade to High Sierra, but probably also before.  "About This Mac" --> "Storage" reports that "System" is using around 180G. But if I check the complete disk, it looks like that:  $ sudo du -cxhd 1 /   0B    /.HFS+ Private Directory Data 1.0K    /home 4.3G    /usr 4.2G    /.Spotlight-V100 1.0K    /net  34G    /nix   0B    /.PKInstallSandboxManager   0B    /.PKInstallSandboxManager-SystemSoftware 2.6M    /bin   0B    /Network 1.1M    /sbin 3.8G    /Library   0B    /.Trashes 6.5G    /System 476K    /.fseventsd du: /private/var/db/ConfigurationProfiles/Store: Operation not permitted du: /private/var/folders/z7/[...]/0/SafariFamily: Operation not permitted du: /private/var/folders/z7/[...]/0/com.apple.LaunchServices.dv: Operation not permitted du: /private/var/folders/z7/[...]/0/com.apple.nsurlsessiond: Operation not permitted du: /private/var/folders/z7/[...]/0/com.apple.routined: Operation not permitted du: /private/var/folders/zz/[...]/0/com.apple.nsurlsessiond: Operation not permitted 8.0G    /private 8.6M    /.DocumentRevisions-V100   0B    /.vol  32G    /Users  11G    /Applications 207M    /opt 5.0K    /dev 4.0K    /Volumes   0B    /cores 104G    / 104G    total   df also says that only 20G are available:  $ df -h / Filesystem     Size   Used  Avail Capacity iused               ifree %iused  Mounted on /dev/disk1s1  234Gi  211Gi   20Gi    92% 4019132 9223372036850756675    0%   /   Any tool I was using (Finder, Disk Inventory X, etc.) shows more or less the same numbers like df and du.  Output of mount:  $ mount /dev/disk1s1 on / (apfs, local, journaled) devfs on /dev (devfs, local, nobrowse) /dev/disk1s4 on /private/var/vm (apfs, local, noexec, journaled, noatime, nobrowse) map -hosts on /net (autofs, nosuid, automounted, nobrowse) map auto_home on /home (autofs, automounted, nobrowse)   I read and tested many, many things like:         ... but with no success. So what could consume more than 100G of disk space without showing up in any tool?  Update  Running „First Aid“ in recovery mode:   What does this error message mean?  error: btn:1: invalid key order (1) oid 440198 / oxid 114577 fsroot tree is invalid.   Update 2018-01-25  Another report of the same error:  (but no answers, yet)  I'm pretty sure this file system error is the root cause for the missing disk space. But I have no idea how to fix that. I was hoping that 10.13.3 would maybe solve it, but it didn't change anything. I guess I need to reinstall... How to determine if string contains specific substring within the first X characters I want to check whether Value1 below contains "abc" within the first X characters. How would you check this with an if statement?  var Value1 = "ddabcgghh";  if (Value1.Contains("abc")) {     found = true; }   It could be within the first 3, 4 or 5 characters. Advantages of ROC curves Understanding Python super() with __init__() methods I'm trying to understand the use of super(). From the looks of it, both child classes can be created, just fine.   I'm curious to know about the actual difference between the following 2 child classes.  class Base(object):     def __init__(self):         print "Base created"  class ChildA(Base):     def __init__(self):         Base.__init__(self)  class ChildB(Base):     def __init__(self):         super(ChildB, self).__init__()  ChildA()  ChildB() Can I use a spell with a casting time of "Bonus Action" as my action? Let $G$ be a group of order $56$. (We do NOT assume the Sylow-$7$ subgroup to be normal.) Then either the Sylow-$2$ subgroup is normal or the Sylow-$7$ subgroup is normal. How to prove?  My idea: consider the case $n_2=7,n_7=8$. Then the number of elements in all Sylow $2$ -subgroups and Sylow $7$-subgroups is at most exactly $(7-1)*8+(2-1)*7+1=56$. This cannot give a contradiction. We need to prove that $G$ is simple. Then $|G||(8!/2)$. To prove $G$ simple, we need to prove there does not exist normal subgroups of order $2$ and order $4$. But I do not know how to prove. Python: using a recursive algorithm as a generator