Problem about real square matrix with rank 1
Eigenvalues of the rank one matrix $uv^T$
How do I get $\cos{\theta} \lt \frac{\sin{\theta}}{\theta} \lt 1$? Why we don't use gamma rays, x-rays or ultraviolet to transmit data? The greater the frequency range of a transmission medium, the greater the number of bits per second it can transmit. In other words, the bigger the bandwidth in hertz available, the bigger the bandwidth in bits per second that can be transmitted.  Given that, why we don't use gamma rays, x-rays or ultraviolet to transmit data instead of e.g. visible(light) in optical fiber or microwaves(cell phones)? CPU Emulation and locking to a specific clock speed If you had read my other , you'll know I've spent this weekend putting together a 6502 CPU emulator as a programming exercise.  The CPU emulator is mostly complete, and seems to be fairly accurate from my limited testing, however it is running incredibly fast, and I want to throttle it down to the actual clock speed of the machine.  My current test loop is this:      // Just loop infinitely.     while (1 == 1)     {                         CPU.ClockCyclesBeforeNext--;          if (CPU.ClockCyclesBeforeNext &lt;= 0)         {             // Find out how many clock cycles this instruction will take             CPU.ClockCyclesBeforeNext = CPU.OpcodeMapper.Map[CPU.Memory[CPU.PC]].CpuCycles;              // Run the instruction             CPU.ExecuteInstruction(CPU.Memory[CPU.PC]);              // Debugging Info             CPU.DumpDebug();             Console.WriteLine(CPU.OpcodeMapper.Map[CPU.Memory[CPU.PC]].ArgumentLength);              // Move to next instruction             CPU.PC += 1 + CPU.OpcodeMapper.Map[CPU.Memory[CPU.PC]].ArgumentLength;                                                 }     }   As you can tell, each opcode takes a specific amount of time to complete, so I do not run the next instruction until I count down the CPU Cycle clock. This provides proper timing between opcodes, its just that the entire thing runs way to fast.  The targeted CPU speed is 1.79mhz, however I'd like whatever solution to the clock issue to keep the speed at 1.79mhz even as I add complexity, so I don't have to adjust it up.  Any ideas? Ubuntu Server 20.04 Nvidia Driver Dependencies I had a hard time installing Nvidia drivers in a fresh install of Ubuntu 20.04.  Installing via sudo apt install nvidia-driver-430 resulted in a list of 542 packages to install.  I ended up spending a bit of manual effort to get the Nvidia-provided driver installed without nearly so many dependencies (only had to install gcc and make).  Is this massive number of dependencies normal for Ubuntu Server?  I did a very vanilla install without the GUI.  Reddit suggested I ask here, as their opinion is that I should just install from the default repos, but I felt that so many packages was absurd just to install a driver.  Edit for clarity: installing the nvidia-driver-430 package appears to install the entire Gnome shell, which I feel is unnecessary on a server. When you attempt to modify a file without having write permissions on it, you get an error:  &gt; touch /tmp/foo &amp;&amp; sudo chown root /tmp/foo &gt; echo test &gt; /tmp/foo zsh: permission denied: /tmp/foo   Sudoing doesn't help, because it runs the command as root, but the shell handles redirecting stdout and opens the file as you anyway:  &gt; sudo echo test &gt; /tmp/foo zsh: permission denied: /tmp/foo   Is there an easy way to redirect stdout to a file you don't have permission to write to, besides opening a shell as root and manipulating the file that way?  &gt; sudo su # echo test &gt; /tmp/foo This post pretty much summarizes my question :   I know for a fact that Mac and Linux are both Unix based  And the commands for Linux should work for Mac, but with limited knowledge for programming I couldn't get it to work.  EDIT: Just saw this -  currently working on it Does anybody know how to add the shapefile name to a field in the file's attribute table?  I've found a description:     'You have to use inline variable in CalculateField like %Name% in   expresssion so that whatever the name of the file is, the string will   be inserted based on Name of the dbase file !'   I've tried to CalculateField tool with %Name%, but I got message:  Executing: CalculateField "2011-11-6 15_41_point" DBFName %Name% PYTHON # Start Time: Thu Dec 08 23:34:23 2011 WARNING 000405: No records within table Succeeded at Thu Dec 08 23:34:24 2011 (Elapsed Time: 1.00 seconds)   Where is my mistake? How does printf with multiple arguments separated by space work I have the following printf function:  $ printf '%s %s %s\t%s\n' 100644 blob 8e1e f1.txt 100644 blob 9de7 f2.txt | git mktree   Can anyone please explain what it produces and why? I expected to have equal number of formatting options %s for each argument string but I have a lot more arguments strings here. When I learned about the Minkowski Space and it's coordinates, it was explained such that the metric turns out to be $$ ds^{2} = -(c^{2}dx^{0})^{2} +(dx^{1})^{2} + (dx^{2})^{2} + (dx^{3})^{2}   $$ where $ x^0,x^1,x^2,x^3 $ come from $ x^{\mu} : \mu = 0,1,2,3 $, and $ c $ is the speed of light. The first resource I had access to--I have to do a bit of digging for the exact paper--of course addressed that this invariant takes the tensor form: $$ ds^2 = g_{\mu \nu}dx^{\mu}dx^{\nu} $$ as well. This two things I've seen in all of my texts and online resources regarding resources. The element in question that varies between authors, is the time coordinate, $ x^0 $. When it was first explained to me, it was using the standard Cartesian representation for the spatial portion of the coordinates, and the time coordinate was labeled as $ x^0 = ict $. Squaring gives $ (x^0)^2 = -c^2t^2 $, and applying differential calculus, we get $ (dx^0)^2 = -c^2dt^2 $. Sensible and expected to have the tensor formula spit out the Minkowski Metric. The author then later explicitly states the coordinates are $ x^0 = ict, x^1=x,x^2=y,$ and $x^3 = z$.  My questions is then, why is it most authors on the subject omit the imaginary unit on the time coordinate? For example, .   The only reason I can fathom omission is if the author is using metric signature $ [+,-,-,-] $, where I started off learning the theory with signature $ [-,+,+,+] $ which may be the reason seeing the time coord with no imaginary unit seems dissonant to me. All help appreciated!  Edit: After reading the other answers, my questions is now one of why and how (mathematically) do we obtain the Minkowski Metric Signature. More specifically the one element with a different sign. Why is boiling water loud, then quiet? Water in my electric kettle makes the most noise sixty to ninety seconds before the water comes to a full boil. I have been fooled many times by the noisy kettle, only to discover that the water was not yet hot enough for tea. The kettle is only at a full boil after the noise has subsided.    I have noticed the same phenomenon with many other kettles, including conventional kettles on kitchen ranges; it is not a peculiarity of this electric kettle.  Why does the boiling become quieter as the water reaches full boil? How to use a variable for a key in a JavaScript object literal? Wayne Dalton Garage So I recent had a Garage door "professional" come out to my house and look at my garage. I originally thought I was having a motor problem because it would only lift door sporadically. After performing a 25 point inspection he believed he located the problem, which was the spring system from my Wayne Dalton Garage (torquemaster). He told me how horrible of a system they are and they don't fix them because of that they only replace the entire system and would cost me $700 or more. So now I'm left trying to figure out what I need, torquemaster springs, bracket assembly, both or if I need something completely else. I need some experience Wayne Dalton experience. Windows 10 thinks it's up to date, but it's not What is the best, easiest, preferably cheapest way to make OS X write to NTFS-formatted drives in Mac OS X? Are upvotes on competing posts counted per question or per answer for Sportsmanship? The definition of the :     Up voted 100 competing answers   doesn't specify whether each upvote on competing answers to the same question counts towards this criteria, or if it's limited to one "point" per question no matter how many additional competing answers you upvote. Can someone explain how it works? Computing $\int_{-\infty}^\infty \frac{\sin x}{x} \mathrm{d}x$ with residue calculus This refers back to $\int_{-\infty}^\infty \frac{\sin x}{x} \mathrm{d}x = \frac\pi2$ already posted. How do I arrive at $\frac\pi2$ using the residue theorem? I'm at the following point: $$\int \frac{e^{iz}}{z} - \int \frac{e^{iz}}{z},$$ and I would appreciate any help. Why does pressing a transform hotkey not display the axes on the selected object? I open Blender 2.80 (official release, not a beta or RC) and get the new scene with the usual 3 objects present (camera, light and cube). I select the cube, press 't' for the tools menu and click on the Move tool. The usual 3 axis glyph appears at the cube's origin as expected. But if I use the hotkey 'g' to activate the move transform instead of selecting the tool from the menu with the mouse this glyph does not appear. The exact same problem exists if I use the a hotkey for rotate or scale as well. Why? Is there some clickable checkbox setting hidden somewhere that could have disabled this? Cannot install a version of GDAL via Anaconda that permits reading BigTIFFs Difference between Inheritance and Composition I'm planning on re-watching the currently-released 5 Marvel films prior to seeing The Avengers.  Have Marvel released any sort of official viewing order?  Captain America: The First Avenger seems like the hardest one for me to place in order with the rest.  It takes place prior to the other films, but has the greatest number of references to the other films.  So should it be watched first, or last?  The rest of them are relatively clear, as they're chronological in the order they're released, with the possible exception of The Incredible Hulk and Iron Man 2 happening at the same time.