Show that $x\otimes x+2\otimes2$ is not an elementary tensor in $I\otimes_{A}I$
$2 \otimes_{R} 2 + x \otimes_{R} x$ is not a simple tensor in $I \otimes_R I$
How to prove $\det(I+uv^\intercal)=1+v^\intercal u$ Let be $u,v\in\mathbb{R}^n$, then $\det(I+uv^\intercal)=1+v^\intercal u $ where $I$ denotes the identity matrix of order $n$. How to prove this?   what I did:   let be $A=\{n\in\mathbb{N}: \forall u,v \in \mathbb{R^n}, \det(I+uv^\intercal)\neq1+v^\intercal u  \} $, and suppose $A\neq \varnothing $, then for the well-orderer-principle there exists $n_0\in A$ such $n_0\leq n,\;\forall n\in A$. since $1\notin A,\; n_0\neq 1 \rightarrow n_0-1\in\mathbb{N}\setminus A  $ so: $$\forall u,v\in\mathbb{R^{n_0-1}}: \det(I+uv^\intercal)=1+v^\intercal u $$ Then, let be $u,v\in\mathbb{R}^{n_0}$, so $$\det(I+uv^\intercal)= \displaystyle\sum_{j=1}^{n_0}(-)^{1+j}a_{1j}\det(A_{1j})$$ where $a_{ij}=\begin{cases} u_iv_j+1 &amp; i=j \\ u_iv_j &amp; i\neq j \end{cases}$, and $A_{1j}$ is the  submatrix of $I+uv^\intercal$ that results deleting the i-file and j-column. Then I try to open the term for $j=1$ and try to use the relation for the new matrix of $n_0-1$ order with the determinant because it holds the same form but I have other terms which difficult me the work. Do you know other method?.  Ps. , in page 2 I've found something similar but I don't understand what it means PS. I'm taking a course of numerical analisys Am I going to have trouble flying with a reversed name on the ticket? I'm flying to Peru with my girlfriend next week and I realized that her name is incorrect on the reservation.  Instead of Sally Marie Jones it's Jones Marie Sally.  We're flying into Houston, then Lima, and in Lima we switch airlines for our flight to Cajamarca.  I booked the ticket with Orbitz who made the reservation with United. United booked the flight with LAN air, the Peruvian airline.  Both companies say that they are unable to change the name because of TSA restrictions not allowing a name change. I asked if I could just cancel and re-book, but United said they could not do this because there are multiple airlines involved.  A note has been attached to the reservation explaining the issue, and the United rep said that they would be able to print her boarding pass with the correct name. However, he said there are no guarantees that she'll be able to fly because although the boarding pass will be correct, the ticket will still have the reversed name.  I was prepared to just take the chance that it will all work out, seeing how it's really obvious the name is just backwards, but with recent events I'm worried that US airport security is going to be extra strict for the next little while.  Is this something I need to worry about, or are chances good that this will work out fine?  The United rep said there's a chance we could cancel the United flights and get a new ticket with the correct name for no cost, but we'd have to pay for new tickets within Peru ($500 out of the total $1300 ticket cost). I'd rather not do this unless there's a reasonable chance we'll have trouble at the airport. Is "National Socialism" always capitalized? So, I'm writing a paper on the rise of communism in China. At one point I write the following:     "Today, it is well known that communism is responsible for more deaths than even national socialism."   Then, Word corrects it by capitalizing "National Socialism."   Is it always meant to be capitalized? I am simply referencing the ideology, not necessarily the Third Reich. Word didn't bother to correct "communism." I suppose since there was only one instance of Nazism (on a national scale at least) it could be considered a proper noun. replacing the default console emulator under Windows XP How can I replace the default program providing console windows under Windows XP?  I know of , and I have a shortcut to start cmd.exe in . But now I want console applications to start in Console2 rather than the default console program, even when I have no control over the program that starts the console application. (I.e. a non-console program starts consoleapp.exe, and I can't change it to start Console2 instead, but I still want the application to be started inside a new instance of Console2.)  (Note that I want to replace the console itself, that is, the window in which console (i.e. text mode) applications run. And I must be able to run arbitrary, unmodified console applications: a substitute for a specific console program such as Cmd won't do me any good.)  EDIT: So what I'm after is a , which           OT: I want to know when Microsoft is going to make a decent CSRSS replacement. Not being able to adjust the width of a "terminal" by resizing the window is a complete joke.         Go download the ISE already. (It's included in Win7/2008R2.)   But as far as I understand this ISE is an , not a general console emulator. Composition of a harmonic function with a holomorphic function is still harmonic If $f$ is a harmonic function in a domain $D \subset \mathbb{C}$, and $g$ is a conformal mapping of a domain $D_0$ onto $D$, is $f \circ g$ harmonic in $D_0$?   I noticed this question while reading several pdf of lecture notes, and I'm having trouble figuring it out. Can anyone help?  Thank you so much! Given that $xyz=1$, prove that $\frac{x}{1+x^4}+\frac{y}{1+y^4}+\frac{z}{1+z^4}\le \frac{3}{2}$ Given that $xyz=1$, prove that $$\frac{x}{1+x^4}+\frac{y}{1+y^4}+\frac{z}{1+z^4}\le\frac{3}{2}.$$  I proved this with , but: is there a better/more elegant way? Determinant of a special $n\times n$ matrix Increasing the maximum number of TCP/IP connections in Linux Tracking Object Position - Firing on a Trajectory So I tried deleting a question, my question. I'm not a mod, but I have reputation above 10k. I received this message after hitting delete, asking me to make sure I wanted to:    But after clicking Delete Question, I saw this:    It turns out that because the question has answers, I'm prohibited from deleting it. If I can't actually delete this question at all, could it just tell me immediately, and only show me the warning if I can actually delete it?  This is akin to the following analogy.     You see a flyer in your local paper stating there's a new burger shop   opening.  Great, you think to yourself, and rush over to get yourself   some burgers.  On your way into the parking lot, you see a huge banner   proclaiming one of their newest burgers. You see some employees walk   in and out of the restaurant, with T-Shirt with pictures of burgers on   them.  Great, you think to yourself, and walk in.   You get in line,   and after what seems like ages, you finally make it to the front.  You   look up at the menu.  You see that they also sell sandwiches. No, you   tell yourself, I'm looking for burgers.  You see that they also sell   burritos! No, you tell yourself, I'm looking for burgers.  Then you   see that they sell burgers. Great! You pick out a burger, then tell   the employee at the register, "Sir, I'd like to get a regular burger   please." Immediately, the employee looks up, with a quizzical look on   his face, saying "Sir? We don't sell burgers here.".   It's the same situation. I've come to that prompt so that I can delete a question.  After repeated messages and windows letting me know the consequences of deleting, what will happen after I have it deleted, I am told that the option of having it deleted by my own hand never existed in the first place. If a superconductor has zero resistance, does it have infinite amperage? Why does Yoda speak the way he does? Yoda's unique speech consisting of reversed grammar is iconic.  Is there any reason he has adopted this speech pattern?  All other alien species encountered seem to have no trouble speaking normally. Why does Yoda speak in this way? How do I login as root? What do I need in order to create an application for ubantu? Uniform convergence on two separate intervals How do I turn off the arrow for desktop icons? I am using Ubuntu 11.10 and my screensaver keeps coming on while I'm watching a movie.  I don't remember this happening in 11.04 and can't remember how to stop it? Binary classification with strongly unbalanced classes How to check if Receiver is registered in Android? Ubuntu installation does not recognize drive partitioning I have a 1TB drive and installed Windows 7 on a 128GB partition.  When I now try to install Ubuntu 11.04 it does not recognize the Windows partition but offers the complete 1TB drive to install Ubuntu on instead. It displays:    However, in the Ubuntu Disk Utility the Windows partitions are recognized.    What do I need to do in order for Ubuntu to recognize the Windows 7 partition and install Ubuntu as a dual boot?   Response to comments  The following commands were executed and the results are shown below:  fdisk -l  WARNING: GPT (GUID Partition Table) detected on '/dev/sda'! The util fdisk  doesn't support GPT. Use GNU Parted.  Disk /dev/sda: 1000.2 GB, 1000204886016 bytes 255 heads, 63 sectors/track, 121601 cylinders Units = cylinders of 16065 * 512 = 8225280 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0x34a38165     Device Boot      Start         End      Blocks   Id  System /dev/sda1   *           1          13      102400    7  HPFS/NTFS Partition 1 does not end on cylinder boundary. /dev/sda2              13       16318   130969600    7  HPFS/NTFS  Disk /dev/sdb: 500.1 GB, 500107862016 bytes 255 heads, 63 sectors/track, 60801 cylinders Units = cylinders of 16065 * 512 = 8225280 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0x14a714a6     Device Boot      Start         End      Blocks   Id  System /dev/sdb1               1       60801   488384001   83  Linux   parted -l  Warning: Unable to open /dev/sr0 read-write (Read-only file system).  /dev/sr0 has been opened read-only. Error: /dev/sr0: unrecognised disk label