Product of Two Random Matrices

  • Zhidong Bai
  • Jack W. Silverstein
Part of the Springer Series in Statistics book series (SSS)


In this chapter, we shall consider the LSD of a product of two random matrices, one of them a sample covariance matrix and the other an arbitrary Hermitian matrix. This topic is related to two areas: The first is the study of the LSD of a multivariate F-matrix that is a product of a sample covariance matrix and the inverse of another sample covariance matrix, independent of each other. Multivariate F plays an important role in multivariate data analysis, such as two-sample tests, MANOVA (multivariate analysis of variance), and multivariate linear regression. The second is the investigation of the LSD of a sample covariance matrix when the population covariance matrix is arbitrary. The sample covariance matrix under a general setup is, as mentioned in Chapter 3, fundamental in multivariate analysis.


Random Matrice Random Matrix Characteristic Sequence Negative Number Vertical Edge 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.School of Mathematics and Statistics KLAS MOE Northeast Normal UniversityChangchunChina
  2. 2.Department of Statistics and Applied ProbabilityNational University of SingaporeSingaporeSingapore
  3. 3.Department of MathematicsNorth Carolina State UniversityRaleighUS

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