Express (10a, a-b, a+5b) as a linear combination of (10, 1, 1) and (0, -1, 5). How do I prove an equation is linear? What does range mean in linear algebra? How to know if there is a nontrivial solution? What ar
Trivial Equation: In mathematics, the term trivial is often used to refer to objects with a very simple structure. Trivial is also used to describe solutions to an equation that have a very simple structure , but for the sake of completeness can't be omitted. ...
Then the solution in algebraic and analytic geometry is to do the local version first, (taking account of the fact that "local" does not mean "locally trivial"), and after that the pointwise version. And tensor products play a crucial role, even in the definiton of vectors and covectors....
If the locally compact group has the no small subgroups property, then one can take to be trivial; thus is Lie, which implies that is locally Lie and thus Lie as well. Thus the assertion that all locally compact NSS groups are Lie (Theorem 10 from Notes 4) is a special case of the...
From a dynamical or group-theoretic perspective, one can also view nilpotent groups as towers of central extensions of a trivial group. Finitely generated nilpotent groups can also be profitably viewed as a special type of polycylic group; this is the perspective taken in this previous blog post...
to the airport by noon. This is a nontrivial challenge on its own. Now imagine you can’t find your glasses (and that you’re as near-sighted as we are). When it comes to solving practical and time-sensitive problems in softwareengineering, observability is a darn good place to start....
As it is shown in the first part of this short essay, duality plus conservation laws allow the violation of Bell’s inequalities for any spatio-temporal separation. To dig deeper into particle dualism, in the second part, a class of models is proposed as a working framework. It encompasses...
Introducing a new dependency into multiple libraries at the core of the PyData ecosystem is a nontrivial exercise however. The above attempts to summarize the state of affairs today. The topic of parallelization is largely an implementation rather than an API question, ...
But, as recently observed by Facchin (2022), such mathematical contents are vulnerable to well-known triviality problems for mapping-theories of physical computation (Sprevak, 2018). The upshot is that the mere availability of mathematical content cannot ground its explanatory relevance. Following (...
We argue though that the crucial difference lies not in the non-linearity of the latter, but in the appearance of non-trivial representation theory related to transcendental extensions of the number field which governs the linear solution. An example is studied to illuminate this point....