Matrix versions of the Cauchy and Kantorovich inequalities
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A version of Cauchy's inequality is obtained which relates two matrices by an inequality in the sense of the Loewner ordering. In that ordering a symmetric idempotent matrix is dominated by the identity matrix and this fact yields a simple proof.
A consequence of this matrix Cauchy inequality leads to a matrix version of the Kantorovich inequality, again in the sense of Loewner.
AMS (1980) subject classificationPrimary 15A45 Secondary 26D15
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