正交规格化一组向量的Gram-Schmidt过程的形式化

IF 1 Q1 MATHEMATICS

Formalized Mathematics Pub Date : 2023-09-01 DOI:10.2478/forma-2023-0005

Hiroyuki Okazaki

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引用次数: 0

摘要

在本文中，我们形式化了Mizar系统[2]，[3]中的Gram-Schmidt过程(比较使用Isabelle/HOL证明助手[1]的另一种形式化)。这个过程是对一组向量进行标准正交化的最著名的方法之一。该方法以Jørgen Pedersen Gram和Erhard Schmidt的名字命名。Gram-Schmidt过程在计算机科学领域有许多应用，例如，纠错码或密码学[8]。首先，我们证明了实酉空间的一些初步定理。接下来，我们形式化了寻找标准正交基的Gram-Schmidt过程的定义。我们遵循[5]的正规化，继续在[7]和[6]中开发工作。

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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On the Formalization of Gram-Schmidt Process for Orthonormalizing a Set of Vectors

Summary In this article, we formalize the Gram-Schmidt process in the Mizar system [2], [3] (compare another formalization using Isabelle/HOL proof assistant [1]). This process is one of the most famous methods for orthonormalizing a set of vectors. The method is named after Jørgen Pedersen Gram and Erhard Schmidt [4]. There are many applications of the Gram-Schmidt process in the field of computer science, e.g., error correcting codes or cryptology [8]. First, we prove some preliminary theorems about real unitary space. Next, we formalize the definition of the Gram-Schmidt process that finds orthonormal basis. We followed [5] in the formalization, continuing work developed in [7], [6].

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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.