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Spectrum and trace invariance criterion and its statistical applications. (English) Zbl 0714.15002
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.
Reviewer: Z.Dostal

MSC:
15A09 Theory of matrix inversion and generalized inverses
15A18 Eigenvalues, singular values, and eigenvectors
62H20 Measures of association (correlation, canonical correlation, etc.)
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