Norm of a Linear Functional for a Positive Definite Quadratic Form

journal6 ›› 2006, Vol. 27 ›› Issue (2): 12-15.

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Norm of a Linear Functional for a Positive Definite Quadratic Form

(College of Computer Science and Mathematics,Jishou University,Jishou 416000,Hunan China)

Online:2006-03-25 Published:2012-09-16

Abstract

Abstract: Let （Ｖ，‖·‖）　be a normed vector space,Ｑ be a positive definite quadratic form on Ｖ,and ｌ be a unit linear functional on Ｖ.The author proves that if the volume of the unit ball of　Ｑ reaches minimum,then Ｑ-norm of ｌ，‖ｌ‖Ｑ≤１,and ‖ｌｉ‖Ｑ＝１ for some special unit linear functionals ｌｉ’s.

Key words: quadratic form, linear functional, inner product, linear transformation, Hausdorff measure

YANG Yu-Ying. Norm of a Linear Functional for a Positive Definite Quadratic Form[J]. journal6, 2006, 27(2): 12-15.

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Norm of a Linear Functional for a Positive Definite Quadratic Form

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