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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. $\endgroup$ –
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.
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.
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 ...
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 31, 2017 · 1) Let a, b, c be not all 0. Then (0, 0, 0) is a trivial solution to the equation ax + by + cz = 0, because you can "see" it at once. 2) To prove that zz¯ = |z|2 for every complex z, the case where z = 0 is a trivial case. 3) The statement that every real number is a real number is a trivial statement.
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?
Jan 3, 2023 · In this light a trivial walk is neither open nor closed. We can say the set of closed walks for a graph G G is a subset of the set of nontrivial walks for G G. But many textbooks do define a closed walk simply as a walk with ending vertex equaling its starting vertex, so that a trivial walk is closed. I do not see a problem with this idea, and ...
