TITLE: What is a "secular equation"?
QUESTION [11 upvotes]: 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!

REPLY [18 votes]: 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."