It only takes a minute to sign up. First up, this question differs from the other ones on this site as I would like to know the isolated meaning of nabla if that makes sense. Meanwhile, other questions might ask what it means in relation to something else. This might be a very stupid question; it's hard to tell when I struggle to understand what it indicates, and thus this might seem very idiotic for a person fully knowledgeable about its meaning.
Currently I interpret the nabla symbol as a way of turning something into a vector.
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Is my understanding correct? Anyway, what is the meaning of it, and why is it used? Please try and describe it as simple as possible. In case there should exist multiple meanings of this symbol, this is the context: I stumbled upon this symbol when researching neural networks C denotes the cost function :.
Nabla is a vector whose components are operators. How you've described it, it's used as the gradient of a function in multivariable calculus. By itself, the nabla can be thought of as a vector of partial derivative operators, and when applied to a multivariable function, it represents the vector of partial derivatives of each component dot product and the direction of steepest ascent for some input:.
The nabla can be applied to a number of different areas in multivariable calculus, such as divergence or curl. In all these cases, the nabla can be treated like a vector which you can dot or cross with another vector, such as a multivariable function. That said, it is an operator. Well, instead of defining these terms directly, let me give the motivation for how they relate to the nabla.
Let's consider the 1D case first, i. Your function itself may have some whacky wavy course that makes it hard to do much with it, but locally i.
This approximation is a truncated Taylor expansion. Its slope is the derivative of the function. Now the dot and cross operations are also short-hand and are labelled as such because they act on vectors in a similar fashion that the respective products do. In simple terms, it is a function that takes in many inputs or vectors and spits out just a real number.
So now we answer the question, "In order to move downhill from my current location, which direction should I move to? Which is the recursive formula for gradient descent that you have probably seen already but the gradient term was scaled by a very small value referred to as the "learning rate".
What this does is make the process take smaller steps in the given direction in order to minimise the chances that it runs past the minimum converging better and not oscillate around the minimum. Now keep in mind that when working with such algorithms, it is very common to see the implementation of heuristic techniques in order to lessen the processing power requirement.Documentation Help Center.
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The dark mode beta is finally here. Change your preferences any time. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. I am working on a report, which contains an equation involved gradient.
So I need the nabla symbol to be printed out like this:. You can find the root cause of such problems by creating a minimal example, i. In your case that would be:. One simple solution would be loading txfonts after fdsymbol. Alternatively, you could update to the more modern newtxtext and newtxmath :. Learn more.
Asked 6 months ago. Active 6 months ago. Viewed 83 times. Thanks a lot! Ralf Stubner Chang Zhao Chang Zhao 11 1 1 bronze badge. Active Oldest Votes. You have to decide yourself if fdsymbol is still needed in this case. Ralf Stubner Ralf Stubner Sign up or log in Sign up using Google. Sign up using Facebook.
I would instead say what it means. So while I may write. The only time I might read the symbols as symbols is if I am performing a computation on the board and am just copying stuff directly from my notes. In those cases I honestly cannot remember what I would usually say.
Alright, I've sort of realized that there is no correct answer to this question. I'm summing up my thoughts and what I've gleaned from the other answers in this CW answer so that I can accept it. It really depends upon context.
Covariant derivatives can have their bases declared beforehand.
So, here is the list of ways of pronouncing stuff:. While reading, it's OK to think of all of these as del I guess. I don't know how relevant this is, but in Brazil, none of those symbols is called "del. This is an interesting discussion. But I have probably not heard it in speech beyond the Australian universities I studied at, so I'm in no position to judge how international is this pronunciation.
BTW, pronounce "dar" so it rhymes with bar, car, far, Mar setc. There is no specific word you'll say it. So you can use anything. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered.The name comes from the Hebrew word for a harpcalled nevelwhich had a similar shape.
Nabla is used in mathematics to denote the del operator, a differential operator that indicates taking gradientdivergenceor curl. It also can refer to a connection in differential geometry and to the backward difference operator in the calculus of finite differencesas well as the all relation most commonly in lattice theory. It was introduced by the Irish mathematician and physicist William Rowan Hamilton in It is the name of an Egyptian harp, which was of that shape". Hamilton and is now in universal employment.
There seems, however, to be no universally recognized name for it, although owing to the frequent occurrence of the symbol some name is a practical necessity.NABLA: indosso e recensisco (quasi) TUTTO!!! + la Dreamy 2!! - Erikioba
In abstract interpretationthe nabla is the usual symbol for the widening operator, an operator that permits static analysis of programs to terminate in finite time. Nabla is used in naval engineering ship design to designate the volume displacement of a ship or any other waterborne vessel.
Where its counterpart, the Greek deltais used to designate weight displacement the total weight of water displaced by the shipthe nabla is used to designate volume displacement, i. Nabla symbol. From formulasearchengine. Hamilton, in Trans. Irish Acad. Thomson, Notes Lect. Willard Gibbs by Edwin Bidwell Wilson Categories : Mathematical symbols Differential operators. Navigation menu Personal tools Log in.
Some of these work just as you'd imagine in LaTeX; type and for parentheses, [ and ] for brackets, and and for absolute value. However, other symbols have special commands:. You might notice that if you use any of these to typeset an expression that is vertically large, like. Some symbols render differently in inline math mode and in display mode.
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It only takes a minute to sign up. I'm writing a summary of a lecture on relativity, and we've recently introduced the Christoffel symbols.
It seems that the upstairs indices are the "leftmost" and the downstairs indices are somewhat right-aligned, at least in print. I found this way of writing them in several works of literature as well as on Wikipedia.
My question thus is:. I know this is more of a LaTeX question, but I guess physicists know more about the core of the question than TeX-perts.
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Horizontal position of indices matters in principle because one might want to raise and lower indices on the Christoffel symbols. If the horizontal position of indices are not observed in a consistent manner, it becomes ambiguous which index was raised or lowered, and so forth, in particular if the connection is not torsionfree. Also note that different authors use different notations and horizontal orderings, e. Sign up to join this community. The best answers are voted up and rise to the top.
Home Questions Tags Users Unanswered. How should Christoffel symbols be written in LaTeX? Asked 4 years, 2 months ago.
Active 4 years, 2 months ago. Viewed 3k times. John W. This also gives you the option to raise and lower the indexes in a natural manner, should you need it. Christoffel symbols are not a "physical" quantity they also appear in pure differential geometry and 2.
Active Oldest Votes. Whenever the indices are not "1 index above a pair of 2", then it must be explained what is the relationship with the normal form of the symbol. Accepted your answer, although I can understand some people wanting to close the question for being off topic. Jan 15 '16 at The Overflow Blog.
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