Inequalities : theory of majorization and its applications

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An order-free characterization along the lines of Horn's theorem is also readily available. Intuitively, if majorizes , then is more "mixed" than. Horn's theorem relates the eigenvalues of a Hermitian matrix to its diagonal entries using majorization. Given two vectors , then majorizes iff there exists a Hermitian matrix with eigenvalues and diagonal entries.

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Portions of this entry contributed by Serge Belongie. Bhatia, R. Matrix Analysis. New York: Springer-Verlag, Horn, R.

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Matrix Analysis, Repr. Cambridge, England: Cambridge University Press, Marshall, A. New York: Academic Press,