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!


1 Answer 1


A secular equation is another name for the characteristic equation.


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



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

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    $\begingroup$ Why it is called secular equation? Is there also a sacred equation? $\endgroup$
    – Popopo
    Mar 20, 2013 at 12:56
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    $\begingroup$ @Popopo See my edits above. $\endgroup$ Mar 20, 2013 at 13:04
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    $\begingroup$ @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. $\endgroup$ Mar 20, 2013 at 13:22
  • $\begingroup$ It's helpful. Thank you. $\endgroup$
    – Popopo
    Mar 20, 2013 at 13:29
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    $\begingroup$ 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. $\endgroup$ Mar 20, 2013 at 13:30

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