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Q: What are Eigenvalues in reasurch?
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Do similar matrices have the same eigenvalues?

Yes, similar matrices have the same eigenvalues.


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How do you find eigenvalues of a 3 by 3 matrix?

Call your matrix A, the eigenvalues are defined as the numbers e for which a nonzero vector v exists such that Av = ev. This is equivalent to requiring (A-eI)v=0 to have a non zero solution v, where I is the identity matrix of the same dimensions as A. A matrix A-eI with this property is called singular and has a zero determinant. The determinant of A-eI is a polynomial in e, which has the eigenvalues of A as roots. Often setting this polynomial to zero and solving for e is the easiest way to compute the eigenvalues of A.


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Do similar matrices have the same eigenvectors?

No, in general they do not. They have the same eigenvalues but not the same eigenvectors.


Can a Hermitian Matrix possess Complex Eigenvectors?

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What has the author Carl Sheldon Park written?

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