square matrices

Important topic: Recall the steps of diagonalizing a matrix A. Step 1 Find eigenvalues of A by finding the roots of the characteristic polynomial det (A- )/) = 0. Specify the multiplicity of each eigenvalue. Step 2 For each eigenvalue A, find a basis of the eigenspace corresponding to 1, i.e. the null space Nul(A - Al). Specify the dimension of each eigenspace. Test: Compare the multiplicity of each eigenvalue with the dimension of its eigenspace. Note that " dimension