.

Also, can you Diagonalize a matrix with complex eigenvalues?

We see that A has only complex eigenvalues λ= § p ¡1 = §i. Therefore, it is impossible to diagonalize the rotation matrix. In general, if a matrix has complex eigenvalues, it is not diagonalizable. In this lecture, we shall study matrices with complex eigenvalues.

Also, can a real symmetric matrix have complex eigenvalues? Another subtle point that may have escaped your attention: all the eigenvalues of these matrices are real. Symmetric matrices can never have complex eigenvalues.

Hereof, can you have complex eigenvalues?

If the n × n matrix A has real entries, its complex eigenvalues will always occur in complex conjugate pairs. This is very easy to see; recall that if an eigenvalue is complex, its eigenvectors will in general be vectors with complex entries (that is, vectors in Cn, not Rn).

What does complex eigenvalue mean?

COMPLEX EIGENVALUES OF REAL MATRICES The characteristic polynomial of an n × n matrix A is the degree n polynomial in one variable λ: p(λ) = det(λI − A); its roots are the eigenvalues of A. If the n × n matrix A has real entries, its complex eigenvalues will always occur in complex conjugate pairs.