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Edit
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Eigenvalues and eigenvectors: Eigenvalues and eigenvectors
The notion of eigenvalue and eigenvector
If \(\vec{v}\) is an eigenvector of the linear transformation \(L\), is it then necessarily also an eigenvector of the composition \(L \circ L\)?
Yes, and the eigenvalue always stays the same.
Yes, but the eigenvalue can be different.
No.
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