Tell me more ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
up vote 3 down vote favorite

Golub mentioned "secular equation" in his Matrix Computation and a slide. However I still don't get its definition. How is a secular equation defined? Thanks!

share|improve this question

1 Answer

up vote 3 down vote accepted

A secular equation is another name for the characteristic equation.

http://en.wikipedia.org/wiki/Characteristic_polynomial#Secular_equation

The reason it is called "secular" is because it was first used in calculations relating the planetary motion:

http://en.wikipedia.org/wiki/Secular_phenomena

http://en.wikipedia.org/wiki/Secular_variation

The etymological root of "secular" is "saeculum," meaning "of an age."

share|improve this answer
1  
Why it is called secular equation? Is there also a sacred equation? – Popopo Mar 20 at 12:56
1  
@Popopo See my edits above. – Jonathan Rich Mar 20 at 13:04
3  
@steveO: secular here means one direction of change with time, as opposed to periodic. If you have $f(t)=at+b \sin t$, the $at$ is the secular part and the $b \sin t$ is the periodic part. – Ross Millikan Mar 20 at 13:22
It's helpful. Thank you. – Popopo Mar 20 at 13:29
1  
An attempt to clarify "secular" vs. "sacred": As far as I know, "saeculum" can mean either "age" or "world". The former meaning leads to secular equations, the latter leads to non-sacred things. – Andreas Blass Mar 20 at 13:30

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.