Topic
Square matrix
About: Square matrix is a research topic. Over the lifetime, 5000 publications have been published within this topic receiving 92428 citations.
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TL;DR: The asymptotic covariance matrix of the sample correlation matrix is derived in matrix form as an application of some new matrix theory in multivariate statistics as mentioned in this paper, where the covariance is derived as a function of the correlation matrix.
23 citations
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TL;DR: In this paper, it was shown that a 2m×2m matrix over k can be factored as ST, with S,T skew-symmetric and S nonsingular, if and only if A is similar to a matrix direct sum B⊕B.
23 citations
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23 citations
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TL;DR: In this paper, the existence of best quadratic unbiased estimators in variance covariance component models is investigated. But the authors only consider a quasinormally distributed random vector y such that Ey = Xβ, Cov y∈L, where L is a linear space of symmetric square matrices.
Abstract: This paper deals with the existence of best quadratic unbiased estimators in variance covariance component models. It extends and unifies results previously obtained by Seely, Zyskind, Klonecki, Zmyślony, Gnot, Kleffe and Pincus. The author considers a quasinormally distributed random vector y such that Ey = Xβ, Cov y∈L, where L is a linear space of symmetric square matrices. Conditions for the existence of a BLUE of Ey and a BQUE of Cov y (Eyy′) are investigated. A BLUE exists iff symmetry conditions for certain matrices are met while a BQUE exists iff some modified quadratic subspace conditions are met. At the end of the paper three examples are studied in which all these conditions are met: The Random Coefficient Regression Model, the multivariate linear model and the Behrens-Fisher model. The proofs of the theorems are obtained by considering linear model in y and yy′, respectively.
23 citations
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TL;DR: In this paper, a sufficient condition for strong shift equivalence for n × n matrices with n > 2 was presented, where the vertices of a directed graph are all n × N nonnegative integer matrices sharing a fixed characteristic polynomial and whose edges correspond to certain elementary similarities.
23 citations