# What is a “secular equation”?

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!

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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."

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Why it is called secular equation? Is there also a sacred equation? –  Popopo Mar 20 '13 at 12:56
@Popopo See my edits above. –  Jonathan Rich Mar 20 '13 at 13:04
@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 '13 at 13:22
It's helpful. Thank you. –  Popopo Mar 20 '13 at 13:29
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 '13 at 13:30