# basis for each eigenspace

#### Sudharaka

##### Well-known member
MHB Math Helper
Hi saqifriends,

Find the eigenvalues using the characteristic equation, $$|A-\lambda I|=0$$. You will get, $$\lambda=2\pm 3i$$. Then for each eigenvalue find the corresponding eigenvectors. The eigenvectors for a given eigenvalue define the eigenspace for that particular eigenvalue. Finally find a basis for each eigenspace.

Some worked examples similar to your problem can be found here. Hope you can continue.

Kind Regards,
Sudharaka.