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Topics in Matrix Analysis by Charles R. Johnson, Roger A. Horn

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        Show that

image

        for all t ϵ [0,1].

        (d)    Now suppose that α is weakly majorized by β, that is,

image

        and suppose that φ(·) satisfies the inequalities

image

        that is, the vector φ(u) is a point in imagek(0) for every u ϵ imagek(L). Show ...

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