scholarly journals Publisher's Note: Phase transitions in the condition-number distribution of Gaussian random matrices [Phys. Rev. E 90 , 050103(R) (2014)]

2020 ◽  
Vol 102 (5) ◽  
Author(s):  
Isaac Pérez Castillo ◽  
Eytan Katzav ◽  
Pierpaolo Vivo
Keyword(s):  
Phase Transitions ◽  
Random Matrices ◽  
Condition Number ◽  
Number Distribution

scholarly journals Deterministic matrices matching the compressed sensing phase transitions of Gaussian random matrices

2012 ◽  
Vol 110 (4) ◽  
pp. 1181-1186 ◽  
Author(s):  
Hatef Monajemi ◽  
Sina Jafarpour ◽  
Matan Gavish ◽  
David L. Donoho ◽  
Keyword(s):  
Phase Transitions ◽  
Compressed Sensing ◽  
Random Matrices

scholarly journals Phase Transitions and Edge Scaling of Number Variance in Gaussian Random Matrices

2014 ◽  
Vol 112 (25) ◽  
Author(s):  
Ricardo Marino ◽  
Satya N. Majumdar ◽  
Grégory Schehr ◽  
Pierpaolo Vivo
Keyword(s):  
Phase Transitions ◽  
Random Matrices

scholarly journals The Exact Distribution of the Condition Number of Complex Random Matrices

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Lin Shi ◽  
Taibin Gan ◽  
Hong Zhu ◽  
Xianming Gu
Keyword(s):  
Random Matrices ◽  
Condition Number ◽  
Random Matrix ◽  
Singular Values ◽  
Exact Distribution ◽  
Wishart Matrix ◽  
Zonal Polynomials ◽  
Wishart Matrices

LetGm×n (m≥n)be a complex random matrix andW=Gm×nHGm×nwhich is the complex Wishart matrix. Letλ1>λ2>…>λn>0andσ1>σ2>…>σn>0denote the eigenvalues of theWand singular values ofGm×n, respectively. The 2-norm condition number ofGm×nisκ2Gm×n=λ1/λn=σ1/σn. In this paper, the exact distribution of the condition number of the complex Wishart matrices is derived. The distribution is expressed in terms of complex zonal polynomials.

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