Random Matrix Theory and its Applications - Lecture 2

Random Matrix Theory and its Applications - Lecture 2

International Centre for Theoretical Sciences via YouTube Direct link

Under this orthonormal transformation

5 of 21

5 of 21

Under this orthonormal transformation

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Random Matrix Theory and its Applications - Lecture 2

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  1. 1 Random Matrix Theory and its Applications: Recap
  2. 2 1. Basics of linear algebra/quantum mechanics
  3. 3 2. Operator
  4. 4 3. Orthogonal transformation
  5. 5 Under this orthonormal transformation
  6. 6 Similarity transformation
  7. 7 4. Eigenvectors & eigenvalues of H Hat
  8. 8 How does one find eigenvalues & eigenvectors?
  9. 9 H Hat =[Hij] -NxN matrix: Matrices with real eigenvectors
  10. 10 Random matrix
  11. 11 Define Random Matrix
  12. 12 Ensembles of random matrices
  13. 13 Wigner matrices
  14. 14 Example
  15. 15 Q: What is the joint distribution of eigenvalues?
  16. 16 Example: Gaussian Ensemble
  17. 17 Rotation invariant ensembles
  18. 18 Under any orthonormal transformation
  19. 19 Example
  20. 20 Exercise: Prove it for NxN case
  21. 21 Q&A

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