Python: How to Replicate a Replicated List Without Cloning
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Least rank of a matrix Let $A$ be a $7\times 7$ matrix such that it has rank $3$ and $a$ be $7\times 1$ column vector.  Then least possible rank of $A+(a a^T)$ is? ($a^T$ is transpose of the vector)  Intuitively I think it's $2$ as $a a^T$ has rank $1$, and the most it could affect is one row of $A$. How to assign the result of the previous expression to a variable? My table is like this:  Sitecode    Month  Amount --------    -----  ------ XX          Jan     1000 XX          Jan     3000 XX          Apr     3000 XX          Apr     1000   What I want is, to show the result something like this:  Sitecode    MonthJAN   MonthAPR --------    --------   -------- XX          4000       4000 What medium should be used for long term, high volume, data storage (archival)? Nominate for Reopening Shows Duplicate Message Boxes I've heard that in the study of finite fields, and other concepts related to finite fields, mathematicians have found a sort of gap: there are various results and things that seem like they correspond to a field with one element, $\mathbf{F}_1$, even though there is no such field. Of course, there is an object which seems similar to a field with one element: the zero ring, $\mathbf{Z}_1$, defined as having one element, $0$, obeying the equations $$0 + 0 = 0 - 0 = 0 \cdot 0 = 1 = 0.$$ The zero ring seems to behave like a field in every respect, except for the fact that it fails to satisfy $0 \ne 1$. (But the importance of the axiom $0 \ne 1$ isn't clear to me.) However, in any case, there seems to be consensus that the zero ring is not the field with one element. People say that the zero ring &quot;does not behave like a finite field&quot; () or that it &quot;does not have the features that mathematicians need&quot; (). I'm not familiar enough with algebraic geometry to understand the properties that $\mathbf{F}_1$ is expected to have. Is there an elementary, undergraduate-level explanation of  why it seems like a field with one element &quot;ought to exist&quot; in the first place, what properties we expect it to have and why, and how the zero ring fails to satisfy these properties?  Or do I need to study algebraic geometry if I want to have an understanding of any of this? (A side question: do we have a good answer to the question of whether the single element of $\mathbf{F}_1$ ought to be $0$, $1$, both, or neither?) How to get the keyboard to input Japanese? Penalized methods for categorical data: combining levels in a factor How can we recover the Newtonian gravitational potential from the metric of general relativity? The Newtonian description of gravity can be formulated in terms of a potential function $\phi$ whose partial derivatives give the acceleration:  $$\frac{d^2\vec{x}}{dt^2}=\vec{g}=-\vec{\nabla}\phi(x)=\left(\frac{\partial\phi}{\partial x}\hat{x}+\frac{\partial\phi}{\partial y}\hat{y}+\frac{\partial\phi}{\partial z}\hat{z}\right)$$  However, in general relativity, we describe gravity by means of the metric. This description is radically different from the Newtonian one, and I don't see how we can recover the latter from the former. Could someone explain how we can obtain the Newtonian potential from general relativity, starting from the metric $g_{\mu\nu}$? When creating the id attributes for HTML elements, what rules are there for the value? When I try to bring down the Achievements tab in Area 51, it's showing an error dialogue.  Strangely enough, the global inbox dropdown works just fine.  Could be connected to .  Screenshot: I am trying to find examples of maps between topological space which are local homeomorphism but not covering maps. Especially, how twisted has to be such a counterexample : can it be a local diffeomorphism between connected manifolds which is not a covering map ?   I found here() a nice proposition which state that a local homeo from a compact space to a connected Hausdorff space is a covering map.   I am interested in all type of counterexamples, from non-Hausdorff spaces to surfaces, to get a better picture of the differences between covering maps and local homeomorphisms.  Thank you ! How to catch the "Login Failed" event? I want to show a custom block, only when log in has failed. So from visibility settings I have to put a PHP code that returns TRUE only when the login has failed.  But how could I "catch" that event? Do I have to use variable_get(..)? And if yes, how could I use that?with what attributes?  Thank you. How to convert std::string to LPCWSTR in C++ (Unicode) Find objects between two dates MongoDB What's the opposite word for "sin"? I would like to know if there is an opposite word for sin in English.  I mean, how could I say the opposite of     I committed a sin   other than using a negation? Single Variable Calculus Reference Recommendations Replacement character being used question URL Some questions, for example    Instead of using a correct URL, such as  http://meta.stackexchange.com/questions/79543/٩●̮̮̃-̃۶-forbid-unicode   are using  https://superuser.com/questions/516363/what-is-the-��-character   What is causing this behavior? Was Yoda wrong about the limits of telekinesis? In Empire Strikes Back, Yoda  that an object's size doesn't matter and that the difficulty of levitating an X-Wing was only in his mind. If the upper limits of telekinesis are determined by belief, what's to stop a Jedi/Sith from pulling a moon out of orbit, moving an entire solar system, or splitting an atom with the Force? Mount USB drive with write permissions for everyone or specific user