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所在平台: Udemy |
课程主页: https://www.udemy.com/course/matrices-and-linear-algebra-college-maths/
课程评论：没有评论
**课程名称：** 探索人工智能中的线性代数 **课程概述：** 本课程由拥有三十多年教学经验的数学教育家 Suman Mathews 博士教授，旨在帮助您更深入地理解线性代数。课程从矩阵的**标准型**入手，讲解如何运用简单的**行变换**将矩阵转化为标准型，并找到两个非奇异矩阵 P 和 Q 使得 PAQ 等于标准型。 随后，您将学习**高斯消元法**和**高斯-约旦消元法**，并理解两者之间的区别，以及在这一过程中**增广矩阵**的概念。 接着，课程将介绍**雅可比迭代法（Gauss-Siedel method）**，并如何利用其解决**对角占优方程组**。您还会学习**对角占优形式**及其转换方法，以及计算矩阵**逆矩阵**的传统方法（伴随矩阵法）。 在深入部分，您将探索**二维和三维变量的线性变换**，以及**正交变换**，并了解与正交变换相关的矩阵被称为**正交矩阵**。**向量的线性无关性**也将在课程中进行讲解。 您将学习如何通过**特征方程**计算矩阵的**特征值**和**特征向量**。此外，课程还将涵盖**凯莱-哈密顿定理**和**矩阵的对角化**。 课程将为您介绍**向量空间**和**子空间**，以及子空间成为向量空间子空间的必要和充分条件。您还将了解**向量在线性代数中的应用**，并学习**向量的正交性**。 **学习目标：** * 掌握矩阵的标准型及其求解方法。 * 理解高斯消元法、高斯-约旦消元法及增广矩阵。 * 学习并应用雅可比迭代法解决对角占优方程组。 * 掌握矩阵逆的计算方法。 * 理解线性变换、正交变换及其矩阵表示。 * 学习向量的线性无关性、特征值和特征向量的计算。 * 掌握凯莱-哈密顿定理和矩阵对角化。 * 理解向量空间、子空间及其属性。 * 了解向量在线性代数中的重要作用。 本课程将为您的人工智能学习之路提供坚实的数学基础，并为您成功学习铺平道路。诚挚邀请您与有需要的同学分享本课程。
You need to learn Linear Algebra in College. It's a fairly interesting topic but a little extra help would be welcome. I am Suman Mathews, math educator and teacher.Having taught Mathematics for over three decades, I hope this course will help you in understanding Linear Algebra better. The course unravels with understanding the normal form of a matrix and how to convert a matrix to it's normal form using simple row operations.You will also learn how to find two non singular matrices P and Q so that PAQ is the normal form. Next, you'll learn about Gaussian elimination method and Gauss Jordan method and the difference between the two. You'll learn what is an augmented matrix in this context.As you proceed with the course, you'll learn about Gauss Siedel method and use it to solve a diagonally dominant system of equations. You'll also learn about diagonally dominant form and how to convert a set of equations to the diagonally dominant form. You'll also learn the traditional method of calculating inverse of a matrix using adjoint.Next you'll learn about linear transformations in two or three variables and regular transformations. Learn about orthogonal transformations and how the matrix associated with an orthogonal transformation is called an orthogonal matrix. You'll dive into linear independence of vectors.Learn about characteristic equation of a matrix and how to calculate eigenvalues and eigenvectors of a matrix using this. So enhance your knowledge with this course on Linear Algebra. Share this with your friends who may need this. Learn about Cayley Hamilton Theorem and diagonalisation of a matrixYou'll be introduced to linear transformations, orthonality of vectors and more. Learn how Vectors are used in Linear Algebra.You'll learn about Vector Spaces and Subspaces. Also learn the necessary and sufficient conditions for subspace of a Vector Space.Create a road map for your success.
