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What is a trivial and a non-trivial solution in terms of linear algebra?
WEBNov 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.
Math.stackexchange.comlinear algebra - What do trivial and non-trivial solution of
WEB$\begingroup$ 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. $\endgroup$ –
Math.stackexchange.comordinary differential equations - What does "trivial solution" mean
WEBJul 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.
Math.stackexchange.comWhat defines "triviality"? - Mathematics Stack Exchange
WEBThere 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
Math.stackexchange.comTrivial zeros of the Riemann Zeta function
WEBTo answer your question, there is a functional equation that the zeta function satisfies: \zeta (s)=2^s\pi^ {s-1}\sin\Big ( \frac {\pi s} {2} \Big) \Gamma (1-s)\zeta (1-s), where \Gamma is the Gamma function. For negative even integers k (-2, -4 et cetera), the sine factor is zero, which makes \zeta (k)=0. Share. Cite.
Math.stackexchange.comLinear algebra terminology: unique, trivial, non-trivial, inconsistent
WEBApr 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.
Math.stackexchange.comConnection between linear independence, non-/trivial and x …
WEBa31x1 + a32x2 + a33x3 = 0; The homogeneous linear system has the two kinds of solutions. 1). zero solution. The sufficient and necessary condition of the zero solution for is listed as follows: det(A) ≠ 0; 2). Non-zero solution: The sufficient and necessary condition of the zero solution is listed as follow: det(A) = 0;
Math.stackexchange.comWhat are trivial functions. - Mathematics Stack Exchange
WEBJan 10, 2019 — I tried searching on net but there were many problems discussing about non trivial function but nowhere its exact definition was given. I found this desmos link, here I thought that g (x) is a non trivial function of x. But g (x) can be written as g (x)=f (8x)=8x-1. Then whats so special about g (x) here.
Math.stackexchange.comlinear algebra - Non-trivial solutions implies row of zeros
WEBMay 30, 2013 — Recall that a system can have either 0 0, 1 1, or infinitely many solutions. Thus, the fact that there is at least one nontrivial solution (other than the trivial solution consisting of the zero vector) implies that there are infinitely many solutions. Thus, your statement is false; as a counterexample, consider the folloring homogeneous
Math.stackexchange.comUse of "Trivially True" in math - Mathematics Stack Exchange
WEBMar 14, 2022 — 1. Generally, "trivial" or "trivially true" can be essentially thought of as meaning "obvious at a glance or with little thought in mind", and a "trivial situation" is one of little importance. As noted above though, it depends on context. What I might consider a triviality worth omitting from proofs in my graduate analysis classes, I might not
Math.stackexchange.com