Mathematics — Linear Algebra · characteristic-polynomial-alternate-definition
Problem
The characteristic polynomial of the square matrix A is usually defined as rA(x)=det(xIn−A). Find a specific relationship between our characteristic polynomial, pA(x), and rA(x), give a proof of your relationship, and use this to explain why Theorem EMRCP can remain essentially unchanged with either definition. Explain the advantages of each definition over the other. (Computing with both definitions, for a 2×2 and a 3×3 matrix, might be a good way to start.)