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Recap: Random matrices with real spectrum
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Classroom Contents
Random Matrix Theory and Its Applications - Lecture 3
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- 1 Recap: Random matrices with real spectrum
- 2 Complex quaternionic matrices
- 3 Other examples of rotationally invariant ensembles
- 4 Exercise: 2x2 - generic orthonormal transit
- 5 Specific orthonormal transit
- 6 Joint distribution of eigenvalues
- 7 Trick - Right set of variables to change
- 8 Remarks
- 9 Rotational Invariant Ensemble
- 10 3x3 - Gaussian case
- 11 Counting degrees of fraction
- 12 Special property of rotationally invariant ensembles
- 13 Real symmetric rotationally invariant ensemble
- 14 Complex Hermitian Case
- 15 Complex Quaternionic
- 16 For rotationally Invariant ensemble =eigenvalues & eigenvectors decouple
- 17 1 d disordered model - GOE and Anderson model
