View Full Version : Lin. Alg.: Prove char. poly. of n-by-n matrix always has....

04-03-2007, 07:05 PM
I was wondering how one would do this. Any explanations would be GREATLY appreciated:

A characteristic polynomial of a matrix A is the polynomial p sub A of x = |xI sub n - A|.

Prove that the characteristic polynomial of an n by n matrix always has degree n, with the coefficient of x^n equal to 1. (Hint: use induction on n)