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所在平台: Udemy |
课程主页: https://www.udemy.com/course/linear-algebra-part-2/
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**Coursera课程概述：线性代数第二部分：向量空间（基与维度）** 本课程深入探讨线性代数的核心概念——向量空间，时长超过9小时。学员将学习向量空间的概念、子空间、向量生成式、线性张成，以及线性相关与线性无关向量和函数。在学习线性相关与无关向量和函数时，重点将放在如何判断向量的线性相关性。此外，课程还将涵盖平凡解与非平凡解的条件，以及子空间的直和。 随后，课程将进入基与维度的介绍。这一部分将引入向量空间研究中的一些基本概念。基被定义为线性无关的生成集。课程内容广泛，包括了矩阵、对称矩阵、厄米矩阵、实数矩阵、可逆矩阵的列等各种情况下的基。同时，学员们还将学会如何确定向量空间和子空间的维度。此外，课程还包含了坐标向量的概念。 本课程还设计了大量的练习题，涵盖了定义、备注、笔记、公理，以及预期出现的例题和带推论的定理。这些练习旨在帮助学员深刻理解和掌握课程内容。 向量空间是线性代数的研究对象，其维度是表征向量空间的关键，维度决定了空间中独立方向的数量。无限维向量空间在数学分析中自然出现，常以函数空间的形式出现，其向量即为函数。 如需任何课程相关帮助，请随时通过站内信联系。完成课程并通过考核后，将获得课程结业证书。
LINEAR ALGEBRA- Part 2 (VECTOR SPACES)BASIS AND DIMENSIONWelcome 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 and Functions. In Linearly dependent and independent vectors and functions 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. The content on Basis for matrices, symmetric matrices, Hermitian Matrices, Real Matrices, Columns of Invertible matrices and many more concepts. This course also provides the knowledge about how to find the Dimensions of Vector Spaces and Subspaces. The concept of Coordinate Vector is also included.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.
