| Additionally we calculate the inner product between eigenvectors to compare the motion displayed in different simulations. |
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| From the calculated eigenfrequencies and eigenvectors, statistical measures of motion can be derived. |
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| In a very natural way, concepts of linear algebra, including eigenvalues and eigenvectors, appear. |
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| Upon diagonalization of C, a set of eigenvalues and eigenvectors is generated defining a new set of generalized coordinates. |
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| Then they sorted the eigenvectors according to the eigenvalues and divided them into three subsets. |
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| There is, however, a way to obtain the kinetic matrix from the experimental eigenvalues and the eigenvectors directly. |
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| Eigenvalues and eigenvectors were computed by Jacobi rotation. |
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| Motions along the first few eigenvectors are mainly large anharmonic fluctuations and generally can be linked to the biological function of proteins. |
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| The DATA matrix is then decomposed using Singular Value Decomposition, which yields the eigenvectors of the covariance matrix. |
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| The eigenvectors of an orthogonal or unitary operator, corresponding to different eigenvalues, are orthogonal. |
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| Centrosymmetric matrices, their basic properties, eigenvalues, and eigenvectors. |
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| Invariant subspaces, cyclic vectors, commutant and extended eigenvectors of some convolution operators. |
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| Eigenvalues and eigenvectors, inner product spaces, diagonalization and quadratic forms take up the middle of the book. |
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| Gaussian elimination and its applications are covered next, followed by eigenvalues, eigenvectors, and determinants. |
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| A pair of matrices share the same set of eigenvectors if and only if they commute. |
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| The sample points are the eigenvalues of a certain unitary matrix, and the weights are the squares of the absolute values of the first components of the eigenvectors. |
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