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This chapter introduces inner products as a special case of bilinear forms. It discusses the representation of an inner product via a symmetric positive definite matrix, the notion of reciprocal basis, and how the presence of an inner product blurs covariance and contravariance.

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Inner Products

  • 章节

  • 发表日期：

    2025年

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  • Ana Cannas da Silva,
  • Özlem Imamoğlu,
  • Alessandra Iozzi

摘要

This chapter introduces inner products as a special case of bilinear forms. It discusses the representation of an inner product via a symmetric positive definite matrix, the notion of reciprocal basis, and how the presence of an inner product blurs covariance and contravariance.