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What are eigenvectors?

What are eigenvectors? Here are some definitions.

Noun
  1. plural of eigenvector
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Eigenvalues and eigenvectors were computed by Jacobi rotation.
Upon diagonalization of C, a set of eigenvalues and eigenvectors is generated defining a new set of generalized coordinates.
The DATA matrix is then decomposed using Singular Value Decomposition, which yields the eigenvectors of the covariance matrix.
In a very natural way, concepts of linear algebra, including eigenvalues and eigenvectors, appear.
Additionally we calculate the inner product between eigenvectors to compare the motion displayed in different simulations.
From the calculated eigenfrequencies and eigenvectors, statistical measures of motion can be derived.

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