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Oct 6, 2015 · What does 'vanishing' mean in the context of Linear Algebra? Ask Question Asked 9 years, 1 month ago.
Oct 6, 2012 · Vanish just means the function is 0 0. Customarily, it means the function has a zero at the point or on the set. I usually just say the function is zero there. Yeah it basically means that the function outputs the value zero at that point. I guess this can be interpreted as a "thick" answer.
Nov 26, 2016 · 3. It is a theorem (probably proven somewhere in the book, but I don't own it) that if the set of zeros of f f has an accumulation point in its domain of definition, then it is identically zero in this domain. Also, you are right - "vanish identically", "identically zero" and "zero for all z ∈ Ω z ∈ Ω " mean the same thing. – Wojowu.
May 28, 2020 · 1. Vanishing: A quantity which takes on the value zero is said to vanish. For example, the function f (z)=z^2 vanishes at the point z=0. For emphasis, the term "vanish identically" is sometimes used instead, meaning the quantity in question does not merely vanish by all appearances, but is mathematically identically equal to zero.
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May 24, 2018 · While reading Haberman's Applied Partial Differential Equations, the topic on self-adjointness, what does it mean that "boundary terms vanish"? More context: "Supposed that u and v are any two functions, but with the restriction that the boundary terms happen to vanish":
Jul 15, 2020 · I am studying Real Analysis by Stein and I don't understand how to interpret the word "vanish", which is used informally in the bounded convergence theorem (Theorem 1.4, pg 56). Here is the theorem for reference and the surrounding comments about it.
2 Answers. Sorted by: 10. Vanish has a sense of suddenness or mystery or finality about it that disappear lacks. In your examples, I would use "disappeared into the house." instead of "vanished into the house." The other two "vanish" examples are fine. I think if you were to change your next example to, "The plane vanished behind a cloud."
Mar 28, 2022 · When does the Hessian on a Riemannian manifold vanish? The Hessian tensor of a smooth function on a Riemannian manifold M with respect to the Levi-Civita connection ∇ is given, globally and in local coordinates {xi}, as: H(f) = ∇(∇f) = (∂2f ∂xi∂xj − Γkij ∂f ∂xk)dxi ⊗ dxj. My question is: when does the Hessian vanish ...
May 13, 2016 · 8. Non vanishing (at, say, p p) means that there is a vector v v in TpM T p M such that αp(v) ≠ 0 α p (v) ≠ 0. Similarly for the k k -form, it means that there is a set of k k vectors such the form is nonzero if evaluated on these vectors. Share.
