The matrix

has a characteristic matrix

and a characteristic polynomial

The three eigenvalues are

The eigenvectors are obtained by putting each eigenvalue in turn into

For ? ₁ = ?1

This can be expanded to yield the linearly independent system

and the solution here is

and

Thus, with an arbitrary selection of x ₂ = 1, the first eigenvector is

For ? ₂ = ?1 + i2,

and when this matrix representation is expanded it is observed that

Here

and

so that with the arbitrary selection of x ₂ = 5, the second eigenvector is

Finally, for ?3 = ?1 ? i2

or in expanded form

Here

and

so that with the arbitrary selection of x ₂ = 5, the third eigenvector becomes

The reader may verify that the three eigenvectors form a linearly independent set.