Eigenvalues Definition and 853 Threads

In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by



λ


{\displaystyle \lambda }
, is the factor by which the eigenvector is scaled.
Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed. Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated.

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  1. D

    To find the energy eigenvalues in the 3D Hilbert space

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  2. X

    I Pauli Spin Operator Eigenvalues For Two Electron System

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  3. M

    A Numerically Calculating Eigenvalues

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  4. M

    Estimating Eigenvalues from linear ODE

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  5. W

    Differential equations with eigenvalues.

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  6. S

    Python How to Correctly Simulate an Infinite Well in Python?

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  7. P

    How Can Dirac Notation Be Used to Determine Eigenvalues and Eigenfunctions?

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  8. B

    I How do i find the eigenvalues of this tough Hamiltonian?

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  9. M

    B Exploring 120-Sided Dice and Eigenvalues

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  10. Mr Davis 97

    Show that given n distinct eigenvalues, eigenvectors are independent

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  11. Mr Davis 97

    Eigenvalues of transpose linear transformation

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  12. J

    MHB What Are the Basics of Eigenvalues and Eigenvectors in Physics Problems?

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  13. H

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  14. N

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  15. Sirsh

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  16. J

    I How are eigenstates and eigenvalues related in quantum mechanics?

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  17. Sirsh

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  18. V

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  19. TeethWhitener

    I Is a symmetric matrix with positive eigenvalues always real?

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  20. J

    A How do I supply arpack drivers with all starting vectors?

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  21. Mr Davis 97

    Show that A and its transpose have the same eigenvalues

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  22. Mr Davis 97

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  23. A

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  24. A

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  25. MrsM

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  27. J

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  28. Mr Davis 97

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  29. D

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  30. H

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  31. D

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  32. L

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  33. D

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  34. Schwarzschild90

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  35. A

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  36. otaKu

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  37. D

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  38. R

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  39. I

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  40. K

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  43. faradayscat

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  44. faradayscat

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  45. SteliosVas

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  46. P

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  47. Amy B

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  48. Dusty912

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  49. D

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  50. E

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