Suppose a matrix $A$ has two distinct eigenvalues
If $A$ has two eigenvalues $\lambda _1, \lambda_2$ and $\dim (E_{\lambda_1})=n-1$, then $A$ is diagonalizable
Instant e-mail notifications of answers to questions I'd like to have Instant notifications by email of answers to my questions.  Can this be implemented? Long, blurry reflections in wet road Secretary problem - why is the optimal solution optimal? I have read about this problem:    But I want to see how it is proven that the "optimal" solution is indeed optimal. I understand how to prove that if the optimal solution is of the form "wait for $t$ candidates and then choose the next best one" then $t=n/e$ is optimal; but why is the best strategy of that form in the first place?  A complete proof is not required - a reference to a good text discussing this is good as well. Create Task in loop but all tasks take the same parameter What exactly is a hat?  I have seen a lot of people arguing the significance of hats and the limited edition hats. I know the hats are sort of linked to the Winterbash stuff, but what exactly is a hat, what does it do, how do I get one?  Is there a full list of hats? Missing settings in GNOME control center installed in Ubuntu MATE I installed GNOME Control Center following  to access Google Drive in Ubuntu MATE 16.04 LTS (MATE desktop environment 1.12.1)   The problem is GNOME Control Center is only showing language support, printers, firewall setup and backups... not online accounts or other settings.  This is what I get:  ~$ gnome-control-center gnome-online-accounts   ** (gnome-control-center:5744): WARNING **: Ignoring launcher landscape-client-settings (missing desktop file)  ** (gnome-control-center:5744): WARNING **: Invalid categories System;Settings; for panel software-properties-gtk.desktop  ** (gnome-control-center:5744): WARNING **: Ignoring launcher ubuntuone-installer (missing desktop file)  ** (gnome-control-center:5744): WARNING **: Could not find settings panel "gnome-online-accounts"   Any ideas?  Thanks! Who fired the shot and what is the symbolism in firing shot right next to Lucas at the end of the movie? At the end of , during the deer hunt, there’s a shot fired right next to Lucas (deliberately missing the shot).   Who fired the shot? Is it Theo's son? What is the meaning of that scene? Is someone warning Lucas that he made a mistake and definitely, Lucas will be punished in the future? Jordan Canonical Form determined by characteristic and minimal polynomials in dimension $3$, but not beyond What is a "loop device" when mounting? How can we recover the Newtonian gravitational potential from the metric of general relativity? How do I identify which Linux distro is running? We have some new hardware in our office which runs its own customized Linux OS.   How do I go about figuring which distro it's based on? In cricket, in UDRS screen, if the ball hits the wicket, then why is not out still given? In cricket, in UDRS screen, if the ball hits the wicket, then why is not out still given?  I saw this situation so many times happened; bowler appealed for UDRS for LBW, in UDRS it shows ball hits the wicket, but still not out is given sometimes. MTMFS consuming an entire CPU core and fans running full bore with Lion You may be aware that Lion introduced MTMFS, the Mobile Time Machine File System.  I've had a couple of instances now where MTMFS has been chewing up an entire core of my dual-core (mid 2009) MacBook Pro for hours on end with no evidence that it's actually doing anything constructive.  As a consequence, CPU temperature rises and the cooling fans run fast and noisy.  Restarting the machine quietened things down again, but I'm expecting it to start again.  Does anyone understand MTMFS well enough to suggest why it's keeping itself busy (or is it most likely, simply a bug), or if there's currently any solution? I fear I may have gone deaf or been scalded to death before Apple release an update... What part of speech does here have in the following sentence?     I am here.   I say that in that sentence, here must be an adverb because:    It modifies the verb am by describing where I am. Am is a “being” verb in this instance, not a “linking” verb.   My friend contends that here is a noun because the word here is, in this instance, defined as this place, which in Merriam-Webster is the definition for the noun here. Proper submodules of Noetherian modules are intersections of indecomposable modules If $M$ is Noetherian, any submodule $N \neq M$ can be written as a finite intersection of intersection-indecomposable ones.   I just don't know how to begin with the proof of this proposition.   Very kind of you for reading or answering. How to prove whether a matrix has rank $1$ If $u$ $∈ \mathbb R^{m \times 1}$ and $v ∈ \mathbb R^{n \times 1}$ how do you show that the $(m \times  n)$ matrix $uv^T$ has rank $1$? Would providing an example be sufficient to prove it? Applications Not Reopening After Restart Bounded in Probability and smaller order in probability I want to supply constant voltage to my LED's but the supply varies from 3.7V to 4.2V (Li-ion battery). I cannot use 3.3V voltage regulator as it will need at least 4.3V voltage at the input but my battery can supply only 4.2V max. so is there any other way I can supply regulated 3.3V to my LED.   RGB LED = 3.3V, 60mA Battery = 3.7V - 4.2V, 3000mA Number of LEDs = 24 The LED's are connected in parallel Create a tar archive split into blocks of a maximum size I need to backup a fairly large directory, but I am limited by the size of individual files. I'd like to essentially create a tar.(gz|bz2) archive which is split into 200MB maximum archives. Clonezilla does something similar to this by splitting image backups named like so:  sda1.backup.tar.gz.aa sda1.backup.tar.gz.ab sda1.backup.tar.gz.ac   Is there a way I can do this in one command? I understand how to use the split command, but I'd like to not have to create one giant archive, then split it into smaller archives, as this would double the disk space I'd need in order to initially create the archive.