For each eigenvalue, we find the eigenspace, which is the kernel of the matrix A - (lamda) I. The eigenvectors associated with each eigenvalue are the nonzero vectors in the eigenspace.
The algebraic multiplicity is determined by looking at the characteristic polynomial
The geometric multiplicity is determined by the dimension of the eigenspace.
An eigenbasis for A is a basis for R^n consisting of the eigenvectors of A.
If an n x n matrix A has n distinct eigenvalues, then there exists an eigenbasis for A.
An n x n matrix A is diagonalizable if and only if there exists an eigenbasis for A.
Section 7.3 - 1, 4, 9, 15, 20, 22, 36, 44
Section 7.4 - 1, 2, 6, 14, 22, 26, 32