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.

- with .
- with .
- with .

EXAMPLE 5. Find the eigenvalues and the corresponding eigenvectors for each of the following matrices.

Department of Mathematics