Every matrix $A\in M_2(\mathbb{C})$ is similar to one of two forms
Classify orbits of conjugating action on $GL_2(\mathbb{C})$
Why could centering independent variables change the main effects with moderation? What's the 'correct' way of registering/installing an Assembly to the GAC? There seems to be lots of different ways to register assemblies with the GAC, as in, they 'work'.  However, what's the "proper" way of doing it?  In response to Lou Franco (and gacutil):  I'm using Gacutil for development, but it seems to me to be not the proper way to install it, since gacutil isn't included in the basic .NET utilities past .NET 1.1 - it's only a developer tool.  Additional: Gacutil (as seen in responses below) is not redistributable, and therefore should not be used in any app that you intend to give to people who are not developers.  AKA, customers.  See .  In response to using WIX:  WIX might be great and all, but how does it work under the hood?  What details makes the way WIX installs the assembly the right way to install it?  How does it look it up?  Is it a system/.NET call?  Is there some call in a dll buried somewhere in System32 that needs to be made?    (Edit: it looks like WIX uses MSI under the hood.  See my comments in the accepted answer.)  Final edit: It looks like the correct way to install an assembly to the GAC is using windows installer, and nothing else.  I'm going to give Wix a try.  Thanks all! align vs equation I always use align in my documents, and avoid equation. Is there anything wrong with that? My reasoning behind this: align > equation, so why not use it? Virtual vs Real image Why did sampling boost the performance of my model? I have an imbalanced dataset with 88 positive samples and 128575 negative samples. I was reluctant to over/undersample the data since it's a biological dataset and I didn't want to introduce synthetic data. I built a Random Forest Classifier with this original dataset. I got an F1 score of 0 for the positive class. Zero precision. Zero recall. I cross-checked the predictions and test data. The model predicts some positives none of which are actually positive. Worst performance.  So, I tried to oversample the positive class. I upsampled the positives to 1000 samples. To my surprise, the F1 score for this dataset was 0.97, for the positive class. Then I tried lesser samples. I was able to achieve an F1 score of 0.83 with 200 positive samples, which is just 2.25 times of the original positive samples.  I would like to know why this occurs. For 88 samples, F1 score is 0.00 (rounded off to two digits). For 200 samples it's 0.83. There is no data leakage. All the features are engineered. I used imbalanced-learn module for oversampling. Can someone explain why is this difference in performance? What is JavaScript's highest integer value that a number can go to without losing precision? Is this defined by the language? Is there a defined maximum? Is it different in different browsers? Often while playing Pathfinder, my group will run into problems where rules for 3-dimensional play simply don't exist, so far as we can find. Arguments will come up over things like carrying-capacity, movement speed, area-effects, and a variety of other things.  Simply put, are there rules for 3D play for Pathfinder, and if so where can I find them? Is there a way to load every label data and every SObject description data using only Javascript without any Apex Server-side code?  How do I import * from @salesforce/schema or @salesforce/label?  I am looking for a way to get all labels or all SObject describe information details to retrieve in LWC at once.  I can see that such syntax is provided by ES6 and is used widely by Salesforce itself, however, it is not possible to use the following syntax in LWC:   import * as schema from '@salesforce/schema'   import * as label from '@salesforce/label'   or this syntax  import {label, schema} from '@salesforce';   since both versions generate error     LWC1512: Missing resource value for @salesforce"   or      LWC1512: Missing resource value for @salesforce/label   Is there a way to load every label data and every SObject description data using only Javascript without any Apex Server-side code?  By the way, if we look as Salesforce Playground we could notice that   the same syntax is used to import everything from lwc  import * as Engine from 'lwc';   however, if we try to insert such line into any of Lightning Web Component, we would receive the following error     LWC1001: Invalid import. Namespace imports are not allowed on "lwc",   instead use named imports "import { LightningElement } from 'lwc'"   or   LWC1517: Invalid LWC import Can we have a perfect field of characteristic $p$ with a non-archimedean valuation? Invoking JavaScript code in an iframe from the parent page Greek pdf bookmarks I am puzzled with sections titled with Greek characters. They do appear in the pdf's Content list, though not correctly.  For example, in my thesis--written in English with LyX, based on the KOMA-script--I choose to include a translation of the summary in Greek (=Περίληψη). The "raw" code for the (unnumbered) chapter title reads: \addchap{\textgreek{Per\char208lhyh}}. In the final .pdf file (using pdflatex) the respective entry appears as Per208lhyh. Using the unicode option for the hyperref package does not fix the problem.  Update detail: the document (should) not only contain Chapter or Section titles in Greek, but normal text as well.  I have found some relevant references within tex.stackexchange and elsewhere (e.g., , the manual of the textgreek package, , ). However, I cannot extract a concrete answer.  How can Greek characters appear correctly as bookmarks in the .pdf's Content list?  Note, the information of this Q&amp;A applies to/under LyX as well. $A$ and $B$ are $n\times n$ matrices and $A+B=AB$. I have an interesting proof that this implies $A$ commutes with $B$, but the proof only works when $||B|| \lt 1$. I'm looking for a way to salvage the proof so that it works for all $B$.  $$A=AB-B$$ $$A=(A-I)B$$ by repeatedly substituting $A$ with $(A-I)B$ on the RHS, $$A= (A-I)B^N - \sum_{i=1} ^{N-1} B^i$$  Since the space of $n\times n$ matrices is Banach (hence complete) under the standard operator norm, the limit $\sum_{i=1}^{\infty}B^i$ is well defined given $||B|| \lt 1$. Hence, taking the limit as $N \rightarrow \infty$, $$A =  -\sum_{i=1}^{\infty}B^i$$  Now the LHS commutes with B, hence so does the RHS.    Is there some trick to extend the method to work with any $B$ where $||B|| \geq 1$? I know that the result is true due to another simple algebraic proof, but I'd like to see if this method can be salvaged. Do spice containers need to be hermetic? Spice containers purchase  I'm planning on upgrading my spice storage. Reading some advice online (e.g. , and ) I came to the conclusion that spice containers should:   Not be exposed to direct sunlight and high temperatures Be airtight   Which means that either you store it inside of some closed cupboard/wardrobe/room or you have containers which do block light and are in a relatively shady place. And the containers need to be airtight.  Available solutions  I've been browsing for some containers available online in my country and the 2 most sensible options I've seen are these:       The problem  The first one is hermetic (it has some rubber around the lid) but it's clear glass. The other one does not have the rubber, just a regular twist-off lid, but it's amber glass.  It'll be hard for me to find any space inside of cupboards to store all of my spices (I need at least 30), so I'd rather buy amber glass container, which I believe will effectively block the sunlight, even when kept on the counter. But I can't find any hermetic amber-glass containers, only ones with regular lid.  The question  Is that regular twist-off lid enough to keep spices airtight and fresh? Or should I focus on buying a hermetic container (like the one in clear glass). I could then for example paint them black to block the sunlight. How do I install a .tar.gz (or .tar.bz2) file? I have downloaded tar.gz files. But I don't know how to install it. How do I install this kind of file? What happens with the force of gravity when the distance between two objects is 0? so I had my first approximation to the gravity equation  \begin{equation} F=GmM/r^2 \end{equation} and some questions arose that my teacher couldnt respond: if r approximates to 0 with mM being constant, then the force should tend to infinity, right? so that being true, then if we would travel to the center of the earth, we would be crushed by gravity? if so, how can there be anything right in the center of the earth? wouldnt anything there be compressed and destroyed by the infinite force?  having that in mind, my next question is as gravity force is measured from the center of an object, any part of the same object which is not at the center would be affected by the same object's gravity? if so, how can we differentiate between two objects that are not in a vacuum? my question originated thinking in us standing on the earth, in contact with it, are we, in a gravitational sense, one object? this lead to the last question, if gravity is a property of matter, then how applying the same logic as before, how does it work between two neutrons?(chose neutrons because i assumed it would be more difficult obtaining gravitational force if there was electrostatic forces from charges inbetween) do two newtrons in contact count as 1 gravitational object? and how thats its own gravity affect the newtron from center and out? Why doesn't Spotlight show invisible files that I know exist? I am running Mac OS X 10.8 (Mountain Lion) and had to edit an invisible file as part of an Android project. While I eventually found it, Spotlight was of no help, since it could not find an invisible file when searching for the exact name (.classpath) and with the 'File Visibility' option set to 'Visible or Invisible'.  Why didn't Spotlight work in this instance? Since the Earth has a magnetic field, can it, in theory, be run through a conductive metal coil to create electricity? Show that $n$ lines separate the plane into $\frac{n^2+n+2}{2}$ regions Show that $n$ lines separate the plane into  $\frac{n^2+n+2}{2}$ regions if no two of these lines are parallel and no three pass through a common point.   I know we start with the base case, where, if we call the above equation P(n), P(0), for 0 lines would be 0.  But I really have no idea how to begin the inductive step.  How do we know what k+1 we're supposed to arrive at?  Thanks! mysql database no space available How can I create light trails without a blurry subject? I would like to achieve this effect using my Nikon P510:      Are there any suggestions or tips that would help me do that?