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

• Mathematics • Previous Articles     Next Articles

Norm of a Linear Functional for a Positive Definite Quadratic Form


  1. (College of Computer Science and Mathematics,Jishou University,Jishou 416000,Hunan China)
  • Online:2006-03-25 Published:2012-09-16

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

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