What is Eigenvalue: Definition and 400 Discussions

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. S

    Find a 2x2 Matrix A for Given Eigenspaces E_2 and E_4

    Find a 2\times 2 matrix A for which E_4 = span [1,-1] and E_2 = span [-5, 6] where E_(lambda) is the eigenspace associated with the eigenvalue (lambda) relevant equations: Av=(lambda)v The Attempt at a Solution I've pretty much gotten most of the eigenspace/value problems down, but this...
  2. S

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  3. Q

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  4. J

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  5. E

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  6. N

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  7. S

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  8. M

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  9. B

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  10. T

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  11. J

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  12. R

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  13. M

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  14. S

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  15. J

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  16. D

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  17. T

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  18. D

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  19. E

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  20. E

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  21. K

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  22. A

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  23. N

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  24. S

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  25. S

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  30. R

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  31. D

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  32. M

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  33. I

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  34. K

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  35. Z

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  36. N

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  37. E

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  41. M

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  42. S

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  43. O

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  44. N

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  45. F

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  46. E

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  47. agro

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  48. P

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  49. S

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  50. E

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