From where the idea of characteristic equations came?

Is there any physical significance of characteristic equations?

Why we always bother about characteristic equation to solve the problem?

What type of problems or difficulties may arise if we don't use Characteristic equation?

Why dividing out the smallest power always produces the characteristic equation?

I am asking all in context Of Recurrence Relation

Is Characteristic equation without any Specific Domain such Calculus, Recurrence Relation etc don't have any meaning?


closed as too broad by Lord Shark the Unknown, TheSimpliFire, Arnaud Mortier, Arnaud D., Ethan Bolker Feb 12 '18 at 12:58

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ I am sorry, more context needs to be provided if you want a good answer. $\endgroup$ – астон вілла олоф мэллбэрг Feb 12 '18 at 6:48
  • $\begingroup$ @астонвіллаолофмэллбэрг I am asking in general(not for any specific type of characteristic equation such as Characteristic Equation for Recurrence Relation etc). $\endgroup$ – Bhaskar Feb 12 '18 at 6:53
  • $\begingroup$ The question could stand with some examples. Un particular, your last question likely means you have only a particular kind of characteristic equation in mind $\endgroup$ – Yuriy S Feb 12 '18 at 7:07
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    $\begingroup$ @Bhaskar : Your question is ambiguous because you don't say to what kind of "characteristic equation" you are thinking of. Did you look at wikipedia ? : en.wikipedia.org/wiki/Characteristic_equation $\endgroup$ – JJacquelin Feb 12 '18 at 8:07
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    $\begingroup$ It as a specific meaning in each domain. That is why one cannot answer without knowing which domain the question refers to. In Mathematics as in other science, it is commun that a word has different meaning depending on the domain. That is why one have to specify the context when the context is not obvious. $\endgroup$ – JJacquelin Feb 12 '18 at 8:57