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More Operator Versions of the Schwarz Inequality

โœ Scribed by Rajendra Bhatia; Chandler Davis


Publisher
Springer
Year
2000
Tongue
English
Weight
42 KB
Volume
215
Category
Article
ISSN
0010-3616

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๐Ÿ“œ SIMILAR VOLUMES


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Let A be an n ร— n positive definite symmetric real matrix with n eigenvalues ฮป 1 , ฮป 2 , . . . , ฮป n and let x and y be two n ร— 1 vectors with the angle ฯˆ. This paper proves the following inequality (x T Ax)(y T Ay).

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Using the theory of connections developed in a paper by Kubo and Ando, operator versions of many classical inequalities are obtained. Finally, it is shown how abstract solidarities, an extension of the Kubo-Ando theory, can be used to obtain operator inequalities.