Spectrum and trace invariance criterion and its statistical applications
type: Item
instance of: scholarly article
title: Spectrum and trace invariance criterion and its statistical applications
zbMATH Open document ID: 0714.15002
DOI: 10.1016/0024-3795(90)90260-J
author: Jerzy K. Baksalary
author: Simo Puntanen
published in: Linear Algebra and its Applications
publication date: 1990-01-01T00:00:00Z
review text: Let \(A,B\in {\mathbb{C}}^{m\times n}\) be rectangular matrices. The authors give a simple condition involving the ranges of A, B and their conjugates which is necessary and sufficient for the set of nonzero eigenvalues of the product \(B^-A\) to be invariant including multiplicities with respect to the choice of a generalized inverse \(B^-\). It turns out that the condition is equivalent to \(tr B^-A\) being invariant. The result is then applied to investigate properties of canonical correlations in the context of the general Gauss-Markov model.
reviewed by: Z. Dostál
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 62H20
zbMATH DE Number: 4175155
zbMATH Keywords: spectrum invariance
zbMATH Keywords: trace invariance
zbMATH Keywords: rectangular matrices
zbMATH Keywords: generalized inverse
zbMATH Keywords: canonical correlations
zbMATH Keywords: Gauss-Markov model
MaRDI profile type: Publication
cites work: Range invariance of certain matrix products
cites work: The matrix inequality \(M \leq B^*MB\)
cites work: Mean square error matrix improvements and admissibility of linear estimators
cites work: Rank invariance criterion and its application to the unified theory of least squares
cites work: Q5618170
cites work: 1-2 inverses and the invariance of \(BA^+C\)
cites work: Matrix Analysis
cites work: A note on multiple and canonical correlation for a singular covariance matrix
cites work: Q3798066
cites work: Q5678319
cites work: Q5556138
cites work: Representations of best linear unbiased estimators in the Gauss-Markoff model with a singular dispersion matrix
cites work: Q3935304
cites work: Q5645536
cites work: Q5181471
cites work: Q3852987
cites work: Linear Least Squares Regression
description: scientific article; zbMATH DE number 4175155