What is Eigen vectors: Definition and 30 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. George Keeling

    How can a diagonalising matrix be unitary?

    This refers to problems A.28/29 from Quantum Mechanics – by Griffiths & Schroeter. I’ve now almost finished the Appendix of this book and been greatly helped with the problems by Wolfram Alpha. In problems A.28/29 we are asked to "Construct the unitary matrix S that diagonalizes T" where T is...
  2. J

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  3. LarryS

    I Eigenvectors - eigenvalues mappings in QM

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  4. S

    I Eigenvectors and inner product

    Hi, what is the physical meaning, or also the geometrical meaning of the inner product of two eigenvectors of a matrix? I learned from the previous topics that a vectors space is NOT Hilbert space, however an inner product forms a Hilbert space if it is complete. Can two eigenvectors which...
  5. dumbdumNotSmart

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    So I ran into an case I have not seen before. Say we have a system of 3 equations such that W´=AW, where W=(x(t),y(t),z(t)) and A is a 3x3 matrix. The way I usually approach these is by finding the eigenvalues of A to then find the eigenvectors and thus find the ¨homogenous¨ solution. What...
  6. B

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  7. G

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  9. H

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  10. K

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  11. B

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  12. dexterdev

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  13. Ravi Mohan

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  14. M

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  15. N

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  16. E

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  17. J

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  18. B

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  19. J

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  20. D

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  21. P

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  22. A

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  23. C

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  24. E

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  25. N

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  26. S

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  28. B

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  29. D

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  30. K

    Understanding Eigen Vectors and Diagonalization for a 2x2 Matrix

    I am trying to find eigen values and eigen vectors for A Its 2X2 matrix. A first row (16 -10) second row (-10 24) I got Eigen values as 30.77 and 9.22 but when i try to find eigen vectors here are the equations I end up with -14.77v1 - 10v2= 0 -10v1 - 6.77v2 = 0 Kinda confused how to...
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