|
所在平台: Udemy |
课程主页: https://www.udemy.com/course/linear-algebra-part-1-vector-spaces/
课程评论：没有评论
**课程名称：** 线性代数 - 第一部分 (向量空间与子空间) **课程概述：** 本课程时长超过9小时，将深入讲解线性代数的基石——向量空间。您将学习： * **向量空间的概念：** 理解向量空间的基本定义、性质及其重要性。 * **向量空间的子空间：** 探索向量空间内的子集，它们本身是否构成向量空间。 * **向量的生成与线性张成：** 掌握如何用一组向量生成整个向量空间，以及线性张成的概念。 * **线性相关与线性无关向量：** 学习判断一组向量是否线性相关或线性无关的方法，这是理解向量空间结构的关键。 * **平凡及非平凡解的条件：** 深入理解线性方程组解的性质。 * **子空间的直和：** 学习如何将向量空间分解为更小的、不相交的子空间。 * **基与维度：** 认识基的定义（一组线性无关的生成向量）及其与向量空间维度的关系，理解维度如何刻画空间的“独立方向数”。 * **无限维向量空间：** 了解在数学分析中为何会出现无限维向量空间，以及函数空间作为其典型例子。 **教学方式：** 课程包含大量的**习题**，涵盖了定义、备注、注意事项、公理、预期中的示例和定理及其推论。这些习题旨在帮助您牢固掌握向量空间和子空间的各个概念。 **课程价值：** 向量空间是线性代数的核心，其维度特征决定了空间内独立方向的数量。本课程将为理解更高级的线性代数概念打下坚实基础，并提供课程完成证书。 **联系方式：** 如对课程有任何疑问，请随时通过私信联系我。
Linear Algebra- Part 1 (Vector Spaces)Welcome to this 9+ hours of course on Linear Algebra where you will learn the Concept of Vector Spaces , Subspaces of Vector Spaces , Generators of Vectors , Linear Span , Linearly Dependent and Linearly Independent Vectors. In Linearly dependent and independent vectors you will learn the concept of how to check whether vectors are linearly dependent or not. Furthermore you will learn the conditions of Trivial and Non Trivial Solutions along with Direct Sum of Subspaces.Then comes the introduction to Basis and Dimension. In this section, some of the basic concepts in the study of vectors spaces is introduced. Basis is a linearly independent spanning set. This course is also subjected with so many Assignments covering the Definitions, Remarks, Notes , Postulates, with all the Expected Examples and Expected Theorems with Corollary. The assignments will helps you to get grasp of the subject.Vector Spaces are the subject of Linear Algebra and are well characterized by their dimension , which specifies the number of independent directions in the space. Infinte-Dimensional vector spaces arise naturally in Mathematical Analysis as function spaces, whose vectors are functions.For any queries related to the course, I would be happy to assist you. Just ping me via Inbox. You will get a course completion certificate after finishing the course.
