Hilbert空间正交分解的形式化

IF 1 Q1 MATHEMATICS

Formalized Mathematics Pub Date : 2022-12-01 DOI:10.2478/forma-2022-0023

Hiroyuki Okazaki

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引用次数: 2

摘要

本文利用Mizar系统[1]，[2]，形式化了Hilbert空间的正交分解定理。对于Hilbert空间H的任何子空间S，任何向量都可以用S中的一个向量与S正交的向量的和来表示。Hilbert空间的正交补的形式化已经存储在Mizar数学库中[4]。我们在形式化中提到了[5]和[6]。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Formalization of Orthogonal Decomposition for Hilbert Spaces

Summary In this article, we formalize the theorems about orthogonal decomposition of Hilbert spaces, using the Mizar system [1], [2]. For any subspace S of a Hilbert space H, any vector can be represented by the sum of a vector in S and a vector orthogonal to S. The formalization of orthogonal complements of Hilbert spaces has been stored in the Mizar Mathematical Library [4]. We referred to [5] and [6] in the formalization.

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来源期刊

Formalized Mathematics MATHEMATICS-

自引率

0.00%

发文量

审稿时长

10 weeks

期刊介绍： Formalized Mathematics is to be issued quarterly and publishes papers which are abstracts of Mizar articles contributed to the Mizar Mathematical Library (MML) - the basis of a knowledge management system for mathematics.