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How to prove a general matrix invertible given by as below?  How to prove that $A^TA+I$ is always invertible for $\forall A \in \mathbb{R}^{n\times n}$? No hyper refs from citation to bibliography using BiBTeX, hyperref and harvard Yesterday, I have downloaded and installed Windows 8 Professional, after downloading it (legally) and burning it to a DVD, on my 3-year-old  (Intel Core Duo 2x2.4&nbsp;GHz, 4&nbsp;GB RAM,  hard disk drive).   The installation failed two or three times, each time differently (error codes, for example 0xc000021a, with an infinite boot loop), but finally I completely formatted the hard drive and installed. Seemingly, everything was OK.  However, after booting successfully, the OS is extremely slow. When I open the task manager, it shows that the HDD is at 100% - however, no application or background process or Windows process can be made responsible. I searched the Internet and found that Windows might try to "index" the hard drive, but I did't find a process that isn't also on my second computer, which still uses the Release Preview (restarting every two hours). Also, the startup is empty, and HD Tune and HDD Health show that the drive health is OK, even though I don't know how reliable these two programs are.  I looked for diagnose software from Toshiba, but they only offer tools for "Fujitsu branded Toshiba devices"; I tried it out, and it did not work on my hard drive.  Does this sound like a hard drive failure? The laptop is 3.5-years-old, has been carried around sometimes roughly and was used (and on) most of the time. However, it would have failed exactly the night before installing Windows&nbsp;8 Profesional, which seems - unlikely.  If this is a software error - then what did I do wrong if this occurs from the moment of installation (even the personalization at the end of installation took half an hour)? How can I fix this? Can't see a glass object through another glass object in Eevee I was just testing Eevee and found that you cannot view a glass object through another glass. Is there any workaround? It works fine only If I rotate the glass window or put my camera to the back side of the scene Is time continuous or discrete? I was coding a physics simulation, and noticed that I was using discrete time. That is, there was an update mechanism advancing the simulation for a fixed amount of time repeatedly, emulating a changing system.  I though that was interesting, and now believe the real world must behave just like my program does. It is actually advancing forward in tiny but discrete time intervals? Underscore doesn't work in Coffeescript's console Most incarnations of The Hulk I've seen or read about state that he is as strong as he needs, basically meaning that there is no limit to how strong he can get.  Is there any canon regarding this? Have we seen the upper limit of the Hulk's strength? Flat quads (or, why is my mesh so funky?) I have a Git repo that I have deleted four files from using rm (not git rm), and my Git status looks like this:  #    deleted:    file1.txt #    deleted:    file2.txt #    deleted:    file3.txt #    deleted:    file4.txt   How do I remove these files from Git without having to manually go through and add each file like this:  git rm file1 file2 file3 file4   Ideally, I'm looking for something that works in the same way that git add . does, if that's possible. Hitting arrow keys adds characters in vi editor When I tried to use arrow keys in insert mode in vi editor the following characters are being inserted in the editor:   for ↓ I get B, for ↑ I get A, for ← I get D, for → I get C.   Please help me in resolve this problem. Using the same secret key for encryption and authentication in a Encrypt-then-MAC scheme Is it a weakness to use a single shared secret for protecting messages using a Encrypt-then-MAC scheme?    Assuming a system is using AES-256-CBC and a SHA1-HMAC and the same secret key for both operations.  Upon intercepting one of these messages and attacker could brute force this secret key by trying to solve the HMAC or by successfully decrypting the first block of the ciphertext.  Performing  a decryption on a single block of AES-256 should be a lighter operation than performing a SHA1-HMAC on a potentially large message.  Therefore AES-256 is ideal for a massively parallel brute-force attack and the use of the SHA1-HMAC doesn't hurt the system.  Is this approach sound, or is there an attack that has not been taken into consideration? How is Anti Aliasing Implemented in Ray Tracing? After reading a few articles online I can confidently say I am clueless on how Anti-Aliasing works when using Ray Tracing.  All I understand is that A Single Pixel/Ray is split into 4 sub-pixels and 4 rays rather than 1.  Could somebody please explain how this is done (preferably with code)? Can you add a separate discussion site? Sometimes you just want to let out some steam, and troll about some technology or software. You are not looking for any answers, but for users with similar experiences and interesting stories. So why not create a separate discussion site (trolling.stackoverflow.com?), where you could ask questions like "why do you hate technology X" or "What are the stupidest bugs you encountered in X"? Grub does not show a Windows 8 option after dual boot Why does the Community User reject / approve edits? What can a soldier requisition and for how long? In the military rank feature it says the soldier can "requisition simple equipment or a horse for temporary use". What qualifies as simple equipment, any simple weapon or something less complex than a catapult?  Additionally, which part of the sentence is the "for temporary use referring to, the simple equipment and the horse or just the simple equipment? On which Stack Exchange site should I post subjective questions? How do I calculate CRC32 of a string How do I calculate the CRC32 (Cyclic Redundancy Checksum) of a string in .NET? On the canonical isomorphism between $V$ and $V^{**}$ I'd love your help with finding the sign of the following integral: $\int_{0}^{2 \pi}\frac{\sin x}{x} dx$,I know that computing it is impossible.  I tried to use integration by parts and maybe to learn about the sign of each part and conclude something but It didn't work for me.  Any suggestions?