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On a special form of the cauchy-schwarz inequality

✍ Scribed by L. Thiele

Publisher: Elsevier Science
Year: 1985
Tongue: English
Weight: 442 KB
Volume: 319
Category: Article
ISSN: 0016-0032
DOI: 10.1016/0016-0032(85)90009-2

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✦ Synopsis

This paper deals with questions concerning a transformation-based form of the Cauchy-Schwarz inequality (f f) (g, g) > (

A g) (g,

) where f and g are complex vectors. In the case ofa linear transformation restricted to be real a rejinement ofthe inequality can be given.

The classes of transformation matrices are defined which impose the equality signs in the above inequalities and thus minimize their left hand sides. A diagonalization procedure provides the determination of a special canonical solution to the desired linear transformation and enables the explicit definition of the remaining degree offreedom.

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