MHB What is the basis for each eigenspace?

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The discussion focuses on determining the basis for each eigenspace by first finding the eigenvalues using the characteristic equation |A-λI|=0, resulting in λ=2±3i. Once the eigenvalues are established, the next step is to find the corresponding eigenvectors, which define the eigenspaces. Each eigenspace is characterized by its eigenvalue and the associated eigenvectors. The conversation also references additional worked examples for further clarification. Understanding these concepts is crucial for effectively determining the basis of each eigenspace.
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saqifriends said:
https://www.physicsforums.com/attachments/215

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.
 
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