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A New Algorithm to Compute the Square Roots of r -circulant Matrices
r-circulant matrices primary square root reduced form Schur decomposition
2012/9/24
A simplified form of r-circulant matrices is investigated , and a new algorithm to compute the square roots of r -circulant matrices is obtained using the properties of r -circulant matrices. In st...
Spectra of Random Hermitian Matrices with a Small-Rank External Source: The critical and near-critical regimes
Spectra of Random Hermitian Matrices Small-Rank External Source
2010/11/24
Random Hermitian matrices are used to model complex systems without time-reversal invariance. Adding an external source to the model can have the effect of shifting some of the matrix eigenvalues, whi...
Toy Model for Large Non-Symmetric Random Matrices
Singular Values Rectangular Random Matrices Free Random Matrix Theory Vector Models
2010/4/28
Non-symmetric rectangular correlation matrices occur in many problems in economics. We test the method of extracting statistically meaningful correlations between input and output variables of large d...
Estimating generalised Lyapunov exponents for products of random matrices
random matrices large-deviation regime fluid flows
2010/4/7
We discuss several techniques for the evaluation of the generalised Lyapunov exponents which characterise the growth of products of random matrices in the large-deviation regime. A Monte Carlo algorit...