2014/10/04 by David Gerard, David C. Gerard, Peter D. Hoff
Computer Science · Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Algorithm #Applied mathematics #Artificial intelligence #Blind Source Separation Techniques #Computer science #Covariance #Decomposition #Generalization #Inference #Kronecker delta #Mathematical analysis #Mathematical optimization #Mathematics #Multilinear map #Order (exchange) #Pure mathematics #Separable space #Singular value decomposition #Statistics #Tensor (intrinsic definition) #Tensor decomposition #Tensor decomposition and applications #Tucker decomposition #math.ST #msc:15A69 #msc:62H12 #msc:62H15 #msc:65F99 #stat.TH
paper · pdf · doi:10.1016/j.laa.2016.04.033
published as Linear Algebra and its Applications 505 (2016) 57--84 · 30 pages
arxiv created 2014/10/04 · openalex publication_date 2016/04/29 · arxiv updated 2018/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We develop a higher order generalization of the LQ decomposition and show that this decomposition plays an important role in likelihood-based estimation and testing for separable, or Kronecker structured, covariance models, such as the multilinear normal model. This role is analogous to that of the LQ decomposition in likelihood inference for the multivariate normal model. Additionally, this higher order LQ decomposition can be used to construct an alternative version of the popular higher order singular value decomposition for tensor-valued data. We also develop a novel generalization of the polar decomposition to tensor-valued data.