Given an eigenvalue , nontrivial solutions of the homogeneous equation are called eigenvectors corresponding to . The null space of is called the eigenspace corresponding to .
Let be scalars. Then the square matrix
In Matlab/Octave, the function diag(a) with column vector a returns the diagonal matrix with diagonal entries given by the vector a. The command
[V,D] = eig(A)returns a diagonal matrix with eigenvalues on diagonal entries, and a matrix whose column vectors are the corresponding eigenvectors.
EXAMPLE 4. Find a basis for the eigenspace corresponding to the value in each of the following.
EXAMPLE 5. Find the eigenvalues and the corresponding eigenvectors for each of the following matrices.