The discussion focuses on proving the characteristic polynomial χA(x) = x² - tr(A)x + det(A) for a 2x2 matrix A. Participants clarify that the left-hand side represents the characteristic polynomial, which is essential in linear algebra for determining eigenvalues. The right-hand side, which includes the trace (tr(A)) and determinant (det(A)) of matrix A, is well understood by the contributors. The goal is to establish the equality by understanding both sides of the equation.
PREREQUISITESStudents studying linear algebra, particularly those working on matrix theory and characteristic polynomials, as well as educators seeking to clarify these concepts for their students.
Chewybakas said:Homework Statement
Let A ε M2x2 prove χA(x) = x^2 -tr(A)x + det(A)
Homework Equations
The Attempt at a Solution
Hi all, this is an assignment equation and the right hand side i can perfectly understand but i can't understand the left hand side, What is it i am looking for?? Can anyone help?