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From Calculus and Analytical Geometry courses, the reader knows that the usual inner product of \(\mathbb {R}^n\) \(\displaystyle \langle \cdot , \cdot \rangle \colon \mathbb {R}^{n}\times \mathbb {R}^{n}\longrightarrow \mathbb {R}~~,~(x,y) \mapsto \langle x,y \rangle := \sum _{j=1}^nx_j y_j, \) where \(x = (x_1, \ldots , x_n)\) and \(y = (y_1, \ldots , y_n)\) , is an essential tool in the construction of the theory.

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Hilbert Spaces

  • 章节

  • 发表日期：

    2025年

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  • Geraldo Botelho,
  • Daniel Pellegrino,
  • Eduardo Teixeira

摘要

From Calculus and Analytical Geometry courses, the reader knows that the usual inner product of \(\mathbb {R}^n\) \(\displaystyle \langle \cdot , \cdot \rangle \colon \mathbb {R}^{n}\times \mathbb {R}^{n}\longrightarrow \mathbb {R}~~,~(x,y) \mapsto \langle x,y \rangle := \sum _{j=1}^nx_j y_j, \) where \(x = (x_1, \ldots , x_n)\) and \(y = (y_1, \ldots , y_n)\) , is an essential tool in the construction of the theory.