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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.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.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.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.comWhat is meant by "nontrivial solution"? - Mathematics Stack …
WEBSep 18, 2021 · This solution would be called trivial. Take matrices, if the square of a matrix, say that of , is , we have A2 =. An obvious (trivial) solution would be =. However, there exist other (non-trivial) solutions to this equation. All non-zero nilpotent matrices would serve as non-trivial solutions of this matrix equation. Share.
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.comP-trivial $\sigma-$algebra - Mathematics Stack Exchange
WEBDec 27, 2020 · Is a random variable constant a.e. iff it is trivial sigma-algebra-measurable? 2 Countably generated sigma algebra vs. generated by a real-valued random variable
Math.stackexchange.comWhat needs to be done to prove that a vector bundle is trivial?
WEBFeb 13, 2019 · 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.
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