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  2. Eigenvalue perturbation - Wikipedia

    en.wikipedia.org/wiki/Eigenvalue_perturbation

    In mathematics, an eigenvalue perturbation problem is that of finding the eigenvectors and eigenvalues of a system = that is perturbed from one with known eigenvectors and eigenvalues =. This is useful for studying how sensitive the original system's eigenvectors and eigenvalues x 0 i , λ 0 i , i = 1 , … n {\displaystyle x_{0i},\lambda _{0i ...

  3. Linear stability - Wikipedia

    en.wikipedia.org/wiki/Linear_stability

    In mathematics, in the theory of differential equations and dynamical systems, a particular stationary or quasistationary solution to a nonlinear system is called linearly unstable if the linearization of the equation at this solution has the form / =, where r is the perturbation to the steady state, A is a linear operator whose spectrum contains eigenvalues with positive real part.

  4. Rayleigh's quotient in vibrations analysis - Wikipedia

    en.wikipedia.org/wiki/Rayleigh's_quotient_in...

    The example shows how the Rayleigh's quotient is capable of getting an accurate estimation of the lowest natural frequency. The practice of using the static displacement vector as a trial vector is valid as the static displacement vector tends to resemble the lowest vibration mode.

  5. Bauer–Fike theorem - Wikipedia

    en.wikipedia.org/wiki/Bauer–Fike_theorem

    In mathematics, the Bauer–Fike theorem is a standard result in the perturbation theory of the eigenvalue of a complex-valued diagonalizable matrix.In its substance, it states an absolute upper bound for the deviation of one perturbed matrix eigenvalue from a properly chosen eigenvalue of the exact matrix.

  6. Rayleigh–Ritz method - Wikipedia

    en.wikipedia.org/wiki/Rayleigh–Ritz_method

    An alternative approach, e.g., defining the normal matrix as = of size , takes advantage of the fact that for a given matrix with orthonormal columns the eigenvalue problem of the Rayleigh–Ritz method for the matrix = = can be interpreted as a singular value problem for the matrix . This interpretation allows simple simultaneous calculation ...

  7. “General Hospital” Kills Off Fan-Favorite Character in ...

    www.aol.com/lifestyle/general-hospital-kills-off...

    General Hospital just bid goodbye to a major character.. During the Friday, Dec. 13 episode, fan-favorite Dex Heller, played by Evan Hofer, met his demise. Dex had been expected to make a full ...

  8. Perturbation theory - Wikipedia

    en.wikipedia.org/wiki/Perturbation_theory

    In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. [ 1 ] [ 2 ] A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. [ 3 ]

  9. Wall St set for higher open as markets await megacap ... - AOL

    www.aol.com/news/futures-march-higher-markets...

    (Reuters) -Wall Street was set to open higher on Monday, with the main U.S. stock indexes poised to recoup some losses following a turbulent trading week, ahead of key corporate earnings and the ...

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