What is the basis for each eigenspace?

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The discussion focuses on finding the basis for each eigenspace associated with the eigenvalues derived from the characteristic equation \(|A-\lambda I|=0\). The eigenvalues identified are \(\lambda=2\pm 3i\). For each eigenvalue, the corresponding eigenvectors are determined, which define the eigenspace. The final step involves establishing a basis for each eigenspace, ensuring a complete understanding of the linear transformations represented by the matrix.

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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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