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Matrix Anal. Appl."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>In this paper we provide the explicit expression and sharper bounds of the chordal metric between generalized singular values of Grassmann matrix pairs. The new results involve the constrained optimization problem of the form $\\max_{U\\in\\mathbb{U}_n} f(U)$, where $\\mathbb{U}_n$ is the set of $n\\times n$ unitary matrices. The optimal solution of this constrained optimization problem is also given. The proposed results can be applied to comparative analysis of gene mRNA expression data for mice macrophage under different conditions in actual experiments on mice. 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