1. Eigenvalue approximations 2 Matrix Computations - Introduction

2. And when the borderline is tau equals zero, the eigenvalues are?

3. Both real and complex semiclassical eigenvalues are obtained that make action variables into integers.

4. This provides superior results if the admittance or impedance matrix of the device has a large eigenvalue spread.

5. We describe an algorithm with which one can verify solutions of an additive inverse matrix eigenvalue problem.

6. The Algebraic multiplicity of an eigenvalue \(\lambda\) of \(A\) is the number of times \(\lambda\) appears as a root of \(p_A\)

7. Tables and graphs of the Eigenvalues are presented for various oblique angles and side-ratios of the parallelogram-pipe.

8. In higher dimensions, steady-state Bifurcations occur at parameter values where the Jacobian matrix has a zero eigenvalue

9. The sum of the sizes of all Jordan blocks corresponding to an eigenvalue λi is its algebraic multiplicity.

10. Critical Buckling load analysis (also known as Eigenvalue Buckling analysis) examines the geometric stability of models under primarily axial load

11. The results then are generalized to give more extended though no fully general conditions for excessive degeneracies in Hückel eigenvalues spectra.

12. The occurrence of Hopf Bifurcations depend on the eigenvalues of the linear portion of (1), given by dz dt (t,μ)=U(μ)z(t,μ)+V(μ)z(t− σ,μ), (2) in which at least one of the eigenvalues of this problem has a zero real part.

13. For non-self-adjoint boundary-value- and eigenvalue-problems of ordinary differential equations variational principles are presented that include the boundary conditions as well.

14. The geodesic Closeness and eigenvalue approaches consider the Closeness of connection to all other actors, but only by the "most efficient" path (the geodesic)

15. Al-though the eigenvalues and eigenvectors for a finite sys-tem may be obtained with less effort from a brute force numerical diagonalization, the Bethe ansatz offers two

16. This solution is asymptotically stable as t → ∞ ("in the future") if and only if for all eigenvalues λ of A, Re(λ) < 0.

17. The Bethe ansatz is an exact method for the calcu-lation of eigenvalues and eigenvectors of a limited but select class of quantum many-body model systems

18. The main feature of this technique is that the original boundary value problem associated with the differential equation is reduced to an algebraic eigenvalue problem.

19. Using an eigenvalue form solution of the equations of motion, a comparison of corresponding numerical results obtained on the basis of all of the afore-mentioned theories is made.

20. As an alternative, and useful for predetermining H∞ gain schedules, the infinity norm is included with the help of ramifications points of the eigenvalue contour of the Hamiltonian matrix.

21. Application of appropriate compatibility conditions to the governing equations of a hyperelastic solid yields an algebraic eigenvalue problem, which determines the possible speeds of propagation and the corresponding directions of the acceleration jump.

22. Course Name (Linear Algebra with Applications ) Code 136.235 Description 136.235 Linear Algebra with Applications 6 credit hours Vector spaces, linear transformations, inner product spaces, eigenvalues and eigenvectors, orthogonal and Hermitian matrices, and applications.

23. In the Born–Oppenheimer approximation, the electronic molecular Hamiltonian is diagonalized on a set of distinct molecular geometries (the obtained eigenvalues are the values of the adiabatic potential energy surfaces).

24. The number of independent invariants ofn×n matricesA, B and their products on which the eigenvalues λ(μ) of the matrix pencilA+μB depend is determined by means of the theory of algebraic invariants and combinatorial analysis.

25. For Kirchhoff's plate a mixed functional is evaluated in which the displacements and velocities are taken to be independent. This method allows an accurate elimination of the displacement parameters and reduces the order of the corresponding algebraic eigenvalue problem.

26. We restrain our considerations to the linear, self-adjoint, constant coefficient case but—in contrast to [1], [9]—we make no assumptions about the nature of the stiff spectrum; the stiff eigenvalues may be arbitrarily distributed on the negative real axis.

27. For center manifolds associated with a purely imaginary pair of eigenvalues the following is shown by classical means: although center manifolds may be nonanalytic the corresponding equations on center manifolds may be treated as if they were analytic.

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29. The Bifurcations discussed above (saddle-node, transcritical, pitchfork, Hopf) are also possible in discrete-time dynamical systems with one variable: \[x_{t} =F(x_{t-1}) \label{(8.35)}\] The Jacobian matrix of this system is, again, a 1×1 matrix whose eigenvalue is its content itself, which is given by \(dF/dx\)

30. The optimal qualities of an algebraic equation corresponding to a self-adjoint homogeneous boundary-value-problem are symmetrical system-matrices, approximation functions without restrictions by boundary conditions, approximation of the eigenvalues from one side and reduction of the order. Combining Ritz's method with that of collocation, the optimal qualities are achieved to a high degree.

31. (Article in which a vector space model was presented) David Dubin (2004), The Most Influential Paper Gerard Salton Never Wrote (Explains the history of the Vector Space Model and the non-existence of a frequently cited publication) Description of the vector space model Description of the classic vector space model by Dr E. Garcia Relationship of vector space search to the "k-Nearest Neighbor" search Bag-of-words model Compound term processing Conceptual space Eigenvalues and eigenvectors Inverted index Nearest neighbor search Sparse distributed memory w-shingling G. Salton , A. Wong , C. S. Yang, A vector space model for automatic indexing, Communications of the ACM, v.18 n.11, pp. 613-620, Nov. 1975