Let Y be an n × p multivariate normal random matrix with general covariance ΣY and W be a symmetric matrix. In the present article, the property that a matrix quadratic form Y′ WY is distributed as a difference of two independent (noncentral) Wishart random matrices is called the (noncentral) generalized Laplacianness (GL). Then a set of algebraic results are obtained which will give the necessary and sufficient conditions for the (noncentral) GL of a matrix quadratic form. Further, two extensions of Cochran's theorem concerning the (noncentral) GL and independence of a family of matrix quadratic forms are developed. © 2010 Elsevier Inc. All rights reserved.
CITATION STYLE
Hu, J. (2010). Equivalent conditions for noncentral generalized Laplacianness and independence of matrix quadratic forms. Linear Algebra and Its Applications, 433(4), 796–809. https://doi.org/10.1016/j.laa.2010.04.010
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