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Matrix versions of the Cauchy and Kantorovich inequalities |
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| Authors: | A. W. Marshall I. Olkin |
| Affiliation: | (1) Department of Statistics, University of British Columbia, 2021 West Mall, V6T 1W5 Vancouver, BC, Canada;(2) Department of Statistics, Stanford University, 94305 Stanford, CA, USA;(3) Department of Mathematics, Western Washington University, 98225 Bellingham, WA, USA |
| Abstract: | Summary 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. |
| Keywords: | Primary 15A45 Secondary 26D15 |
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