Why is this an eigenvector of this matrix?
How Do I Compute the Eigenvalues of a Small Matrix?
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 10 hour layover in Moscow Russia, do I need a transit visa? On June 29th 2015, I will be traveling for the first time to Italy from USA. I will have a 10 hour layover in Moscow Russia. My question is, do I need a visa to visit the city? Please tell me is there any fundamental difference between the two sentences:   Even today, people continue to use cheques.  Even today, people are continuing to use cheques.    I mean is there a difference as in time period (i.e when the action starts and when it ends). Or are the two sentence just the same and interchangeable? When is it acceptable to call GC.Collect? The general advise is that you should not call GC.Collect from your code, but what are the exceptions to this rule?  I can only think of a few very specific cases where it may make sense to force a garbage collection.   One example that springs to mind is a service, that wakes up at intervals, performs some task, and then sleeps for a long time. In this case, it may be a good idea to force a collect to prevent the soon-to-be-idle process from holding on to more memory than needed.   Are there any other cases where it is acceptable to call GC.Collect? How to revert a do-release-upgrade? I can update my Ubuntu to the new LTS version. As you can think, its not a highly important server since I run 13.10 (not a LTS version). Anyway - I actually want to upgrade my server, but would like to be able to revert this upgrade.   I would be able to reinstall Ubuntu 13.10 and overwrite it with my backup. But I want to know if there is a more comfortable way to do this. TBH I guess theres no command as undo-release-upgrade but I thought it would be worth to ask for it.  This is my current daily backup script  tar cvpzf $backup_file --exclude=/proc --exclude=/lost+found --exclude=$backup_file --exclude=/mnt --exclude=/sys --exclude=/media --exclude=/tmp / What is the resolution I need to make a picture to make curves look smooth and not pixelated? Where can I download Windows 8 legally, from Microsoft? Why is "chmod -R 777 /" destructive? This is a  about File Permission and Why 777 is "destructive".   I'm not asking how to fix this problem, as there are a ton of references of that already on Server Fault (reinstall OS). Why does it do anything destructive at all?  If you've ever ran this command you pretty much immediately destroy your operating system. I'm not clear why removing restrictions has any impact on existing processes. For example, if I don't have read access to something and after a quick mistype in the terminal suddenly I now have access well... why does that cause Linux to break? Is C++ CLI a superset of C++? Would a C++  compiler be able to compile some large sets of C++ classes without modifications?   Is C++ CLI a superset of C++? The  badge seems like a great candidate for a trackable badge: it requires doing a thing multiple times, there aren't any other requirements to get it, and it is (seems?) quite easy to determine how many times the thing has been done.  But Convention does not appear in the list of badges that can be tracked. I would like to be able to see a quick count of my well-received meta posts without going to my meta user activity page and poking around. Why don’t photons interact with the Higgs field and hence remain massless? I just try to visualize some points using GeoServer to publish them as WMS and bind this WMS to my Openlayers website using the GeoServer internal Heatmap process to visualize it. I don't want to use the Openlayers Heatmap function.   But there seem to be some problems, look here:    I'm using this Openlayers implementation to bind my WMS URL:    Changing the params to:  params: {'LAYERS': 'test:points','TILED': true,'STYLES': 'heatmap'},   And using this as SLD to define the Heatmap:    Any ideas why this happens? Geometric interpretation of $\frac {\partial^2} {\partial x \partial y} f(x,y)$ This was an assertion made in our textbook but I have no idea how to show that either statement is true.  Also would like to show that that $\mathbb{Q}(\sqrt{2})$ is strictly larger than $\mathbb{Q}$, which was the second part of the assertion. Prove that $\frac d {dx} x^n=nx^{n-1}$ for all $n \in \mathbb R$.   I saw some proof of $\frac d {dx} x^n=nx^{n-1}$ using binomial theorem, which is only available for $n \in\mathbb N$. Do anyone have the proof of $\frac d {dx} x^n=nx^{n-1}$ for all real $n$? Thank you. PostgreSQL CPU 100% after configure Wal log shipping hot standby I have configured Hight Avaliabily WAL Log Shipping Hot Standby (SSL) with one node. But after I configure, both hosts (primary and secondary) take 100% CPU usage. The most strange is because I have only one database called &quot;TESTE&quot; with one table called &quot;EXAMPLE&quot; to check if replication was OK. The replication worked perfectly but I don't understand why my CPU takes 100% usage because I don't have any application connect on my cluster. I ran HTOP command and get this results: Image 1 - Primary Server HTOP Info  Image 2 - Secondary Server HTOP info  S.O. version: No LSB modules are available. Distributor ID: Debian Description:    Debian GNU/Linux 10 (buster) Release:        10 Codename:       buster  PostgreSQL version: postgres (PostgreSQL) 12.3 (Debian 12.3-1.pgdg100+1)  Primary server postgres.conf file: max_connections = 100 SSL = on shared_buffers = 2GB work_mem = 10485kb maintenance_work_mem = 512MB dynamic_shared_memory_type = posix effective_io_concurrency = 200 max_worker_processes = 4 max_parallel_maintenance_workers = 2 max_parallel_workers_per_gather = 2 max_parallel_workers = 4 wal_level = replica wal_buffers = 16MB max_wal_size = 200MB min_wal_size = 80MB checkpoint_completion_target = 0.7 archive_mode = on max_wal_senders = 3 wal_keep_segments = 8 hot_standby = on hot_standby_feedback = on random_page_cost = 1.1 effective_cache_size = 6GB default_statistics_target = 100  pg_stat_activity info:  pg_stat_archiver info:  pg_stat_replication info:  If I stop postgres service in both servers the CPU still has 100% usage. Anyone can help me? How to tile textures in Cycles? If the $n^{th}$ partial sum of a series $\sum a_n$ is $S_n = \frac{n-1}{n+1}$, find $a_n$ and the sum. When I go to localhost/phpmyadmin I get the apache "Not Found" error (404). However, I can load html pages, and run php pages (such as &lt;?php phpinfo(); ?&gt;). And phpmyadmin is installed.  balter@homedevbox:~$ aptitude search phpmyadmin i   phpmyadmin                                               - MySQL web administration tool   I also installed the standard ubuntu LAMP stack and set passwords for mysql and all that.  What could be the problem?  EDIT: Here is where my phpmyadmin files are.  balter@homedevbox:/var$ cd / balter@homedevbox:/$ sudo find . -type d -name phpmyadmin ./var/lib/mysql/phpmyadmin ./var/lib/phpmyadmin ./etc/phpmyadmin ./usr/share/phpmyadmin ./usr/share/dbconfig-common/scripts/phpmyadmin ./usr/share/dbconfig-common/data/phpmyadmin ./usr/share/doc/phpmyadmin Creating a selector from a method name with parameters I have a code sample that gets a SEL from the current object,   SEL callback = @selector(mymethod:parameter2);   And I have a method like    -(void)mymethod:(id)v1 parameter2;(NSString*)v2 { }   Now I need to move mymethod to another object, say myDelegate.  I have tried:  SEL callback = @selector(myDelegate, mymethod:parameter2);   but it won't compile.