| Hence, the three eigenvalues would be complex numbers that lie somewhere in the complex plane within the areas defined by those circles. |
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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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| Then they sorted the eigenvectors according to the eigenvalues and divided them into three subsets. |
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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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| Do you realize that's the pair-correlation function for the eigenvalues of a random Hermitian matrix? |
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| In a very natural way, concepts of linear algebra, including eigenvalues and eigenvectors, appear. |
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| It was a matter of estimating eigenvalues of non-self-adjoint differential equations and matrices. |
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| In particular he proved results on the existence of matrices with given eigenvalues and given diagonal elements. |
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| Weinstein's method was developed to give accurate bounds for eigenvalues of plates and membranes. |
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| This is where those eigenvalues of random Hermitian matrices enter the picture. |
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| The protected polymorphism conditions are now given by the inequalities that the absolute values of these eigenvalues are larger than one. |
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| The eigenvalues of the first bending and twisting modes of a structure are directly related to the flexural and torsional stiffness, respectively. |
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| In those cases, we see two eigenfunctions with approximately the same statistical wavelength and usually with similar eigenvalues and relative spectral power. |
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| He showed that in this case the integral equation had real eigenvalues, and the solutions corresponding to these eigenvalues he called eigenfunctions. |
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| In August 2003 the computer program made conjecture 1001 stating that for any benzenoid graph, the size of a maximum matching equals the number of positive eigenvalues. |
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| Gaussian elimination and its applications are covered next, followed by eigenvalues, eigenvectors, and determinants. |
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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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| If A is an n x n Hermitian matrix, then it is well known that all the eigenvalues of A are real. |
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| With eigenvalue-one criterion, components with eigenvalues greater than 1 are retained. |
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| Wigner also discovered that the statistics of gaps can be modelled by eigenvalues of large random matrices. |
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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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| Although the convergence results apply only for the case of real distinct eigenvalues, we also perform numerical tests involving complex conjugate pairs. |
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| When one tensor is strictly copositive, the complementarity eigenvalues can be computed by solving polynomial optimization with normalization by strict copositivity. |
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| Eigenvalues and eigenvectors were computed by Jacobi rotation. |
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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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