Standards: Chapter 6

Given a matrix A and an eigenvalue λ of A, I can compute the
eigenspace of λ. I can show that the eigenspace is a subspace.

I can compute the characteristic polynomial of any block upper
triangular matrix with 2x2 or 3x3 blocks on the diagonal. Given a
factored characteristic polynomial of a matrix, I can compute the
eigenvalues and eigenvectors of a matrix. I know the relationship
between the dimension of an eigenspace and the multiplicity of an
eigenvector.

I can compute the eigenvalues and eigenspaces of a linear
transformation T in dimensions 2 or 3 that is described
geometrically.  

Given an nxn matrix A with with n linearly independent
eigenvectors, I can describe the linear transformation associated to A
geometrically in the case that n = 2 or 3.  

I understand why an nxn matrix A matrix is diagonalizable if and only
if A has eigenvectors that form a basis for R^n. Given a nxn matrix A
that has eigenvectors that form a basis for R^n, I can diagonalize A.

I can explain why eigenvectors for distinct eigenvalues are linearly
independent.