basis for each eigenspace

[saqifriends]

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[Sudharaka]

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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.