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- Dictionarytriv·i·al/ˈtrivēəl/
adjective
- 1. of little value or importance: "huge fines were imposed for trivial offenses" Similar Opposite
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Nov 8, 2016 · Trivial solution is a technical term. For example, for the homogeneous linear equation $7x+3y-10z=0$ it might be a trivial affair to find/verify that $(1,1,1)$ is a solution. But the term trivial solution is reserved exclusively for for the solution consisting of zero values for all the variables. There are similar trivial things in other topics.
8. There are two meanings of the word "trivial" in mathematics. The first, as you rightly pointed out, is strictly defined and appears in most mathematical fields. By strictly defined, I mean that if you say "the trivial solution to the ODE y′ = g(x)y y ′ = g (x) y ", I know with certainty that you mean the solution y ≡ 0 y ≡ 0.
$\begingroup$ Since the zero solution is the "obvious" solution, hence it is called a trivial solution. Any solution which has at least one component non-zero (thereby making it a non-obvious solution) is termed as a "non-trivial" solution. $\endgroup$ –
Oct 10, 2015 · A trivial solution is just only the zero solution and nothing more. In ordinary differential equations, when we way that we are looking for non-trivial solutions it just simply means any solution other than the zero solution. In your example, the trivial solution is. u(x) = 0, for all x in domain of interest u (x) = 0, for all x in domain of ...
Jul 1, 2019 · X = X is a trivial answer [more in the first part of my definition above] In applied mathematics using operations research [0,0,0] will often be a trivial answer because we would never want an instance of nothing happening.Yet mathematically [0,0,0] is possible. Getting an answer with a negative physical amount is often trivial.
Sep 18, 2019 · The link says, that a LTU can be represented when the expression is trivial and cannot be represented when it is non-trivial (page3). That's not what it says. First, you've mixed up what the role of LTUs is here.
Sep 18, 2021 · Usually, the 0 0 -vector as a solution of a homogenous equation is called the "trivial solution". Any other solution is therefore "nontrivial". To expand on the comment of @Peter, the reason for using the word "trivial" in that context is that it takes a trivial amount of effort to verify that 0 0 is a solution of any homogeneous equation.
Jul 17, 2015 · 5. I've been operating happily under the definition that a nontrivial graph is a graph with at least two vertices for some time. Today I came upon a source which defined a nontrivial graph as a graph with one or more edges. Now I have all my ruffles in a bunch. What is the most widely accepted definition of a nontrivial graph?
This an extension to @Dietrich's answer. The convergence of the above summation, using the alternating zeta (or "Dirichlet's eta"), based on the terms of the series can be much improved using Euler-summation to some order.
Jul 9, 2011 · $\begingroup$ Please define your terms; this is hopelessly confusing. Some people use "Empty graph" to mean a graph with no edges that may still have nodes. You've said "the trivial graph" is the one with just one vertex, but it's not clear whether you're intending "empty graph" to mean the same thing as "trivial graph" in that sense. $\endgroup$
