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- W1995149064 abstract "Through a Hermitian-type (skew-Hermitian-type) singular value decomposition for pair of matrices (A, B) introduced by Zha (Linear Algebra Appl. 1996; 240:199–205), where A is Hermitian (skew-Hermitian), we show how to find a Hermitian (skew-Hermitian) matrix X such that the matrix expressions A − BX ± X*B* achieve their maximal and minimal possible ranks, respectively. For the consistent matrix equations BX ± X*B* = A, we give general solutions through the two kinds of generalized singular value decompositions. As applications to the general linear model {y, Xβ, σ2V}, we discuss the existence of a symmetric matrix G such that Gy is the weighted least-squares estimator and the best linear unbiased estimator of Xβ, respectively. Copyright © 2007 John Wiley & Sons, Ltd." @default.
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- W1995149064 date "2007-09-04" @default.
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- W1995149064 title "More on extremal ranks of the matrix expressions <i>A</i> − <i>BX</i> ± <i>X</i> <sup>*</sup> <i>B</i> <sup>*</sup> with statistical applications" @default.
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- W1995149064 doi "https://doi.org/10.1002/nla.553" @default.
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