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- Dictionarytrivial/ˈtrɪvɪəl/
adjective
- 1. of little value or importance: "huge fines were imposed for trivial offences" Similar Opposite
- 2. denoting a subgroup that either contains only the identity element or is identical with the given group.
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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.
$\begingroup$ 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. $\endgroup$ –
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 ", I know with certainty that you mean the solution y ≡ 0. The same goes for trivial ...
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 31, 2017 · Depending on the context, trivial solutions can be: the zero function y = 0 y = 0. singular solutions of the differential equation (e.g. where you divide by 0 0 in the process of solving the differential equation) constant functions y = c, c ∈ R y = c, c ∈ R. or just solutions which one can see immediately.
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.
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?
Sep 18, 2021 · I think of the trivial case as the case that invariably arises as the problem’s parameters vary. In particular, the trivial solution of a homogeneous system of linear equations is the zero vector. Share
Apr 5, 2015 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
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.
