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所在平台: Udemy |
课程主页: https://www.udemy.com/course/computational-linear-algebra-with-python-numpy/
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课程名称：使用 Python 和 NumPy 的计算线性代数 课程概述：欢迎参加使用 Python 和 NumPy 的计算线性代数课程。这是一个全面的线性代数教程，针对数据科学家和机器学习工程师，涵盖基础概念、实际应用以及真实世界的应用，旨在增强您在该领域的理解和专业技能。该课程将线性代数与 Python 编程相结合，是希望在提高数学知识的同时提升编程技能的学习者的理想选择。 在课程的介绍部分，您将学习线性代数的基本概念及其实际应用。随后，您将进入第一课，深入了解标量、向量和矩阵等基本概念，并学习矩阵的加法、减法和乘法操作。在第二课中，您将手动计算矩阵的逆和转置，并使用 NumPy 进行计算。接下来，在第三课中，您将学习如何计算 2x2 和 3x3 矩阵的行列式，此外还会解释如何解决复杂的线性方程组，通过多种练习题来巩固理解。第五课将介绍特征值和特征向量的计算方法。 在第六课中，您将了解线性分解，特别是 LU、QR 和 Cholesky 分解，并进行手动计算和 NumPy 使用。第七课将让您学习如何用 NumPy 创建特定大小的张量，并掌握切片和索引技术以访问张量的值。在第八课中，您将手动和使用 NumPy 进行奇异值分解的计算。 完成线性代数课程后，您将有机会将所学概念应用于五个实际项目，分别是构建基于线性分解的推荐系统、使用奇异值分解的图像压缩、预测房地产市场的线性回归、使用非负矩阵分解进行文本挖掘以及使用主成分分析进行降维。 学习计算线性代数的理由在于，线性代数是机器学习、数据科学和工程中许多高级数学概念和技术的基础。它在理解和实施线性回归、支持向量机和神经网络等算法方面具有重要作用，同时也能够帮助我们高效分析大型数据集、进行降维和解决优化问题。 课程学习内容包括： - 理解线性代数的基本概念及其现实世界应用 - 理解标量、向量、矩阵和张量的区别 - 使用 NumPy 进行矩阵加法、减法和乘法操作 - 计算矩阵的逆、转置和行列式 - 使用 NumPy 解决线性方程组 - 计算特征值和特征向量 - 学习 LU、QR 和 Cholesky 分解 - 创建、切片和重塑张量 - 实际项目开发经验，例如构建推荐引擎、图像压缩、房地产市场预测等 这个课程为您提供了一个完美的机会去掌握计算线性代数，并在实践中将其应用于真实世界的情境中。
Welcome to Computational Linear Algebra with Python & Numpy course. This is a comprehensive linear algebra tutorial for data scientists and machine learning engineers, this course will cover fundamental concepts, practical implementations, and real-world applications to enhance your understanding and expertise in the field. This course is a perfect combination between linear algebra and python, making it an ideal opportunity for anyone who is looking to practice their programming skills while improving their mathematical knowledge. In the introduction session, you will learn the basic fundamentals of linear algebra, such as getting to know its use cases and key concepts. Then, in the next section, we will start the first lesson where you will get to know more about the basic concepts like scalar, vector, and matrices. In addition, you will also learn about matrix operations like addition, subtraction, two by two matrix multiplications, and three by three matrix multiplications. Afterward, in the second lesson, you will learn how to perform inverse and transpose on matrices manually, then after that you will also learn how to use Numpy to do the calculation. In the third lesson, you will learn how to calculate determinants of two by two matrices and three by three matrices both manually and using Numpy. Then, in the fourth lesson, you will learn how to solve complex linear equations and to make sure you understand the concepts, we will try many practice problems. Meanwhile, in the fifth lesson, you will learn how to calculate eigenvalues and eigenvectors both manually and using Numpy. Then, in the sixth lesson, you will learn about linear decomposition particularly LU, QR, and Cholesky decomposition. Firstly we will do the calculation manually then after you understand the basic concepts, then we will utilize Numpy for computations. After that, in the seventh lesson, you will learn how to create a tensor with specific size using Numpy and even more exciting, we will play around with the tensors and learn how to access a value of tensor by using slicing and indexing techniques. Then, in the eighth lesson, you will learn how to calculate singular value decomposition both manually and also using Numpy. After we are done with linear algebra lessons, we will make sure that you have the opportunity to implement all concepts that you have learnt into real world projects. In total, there will be five projects, in the first project, you will build recommendation engine using linear decomposition, in the second project, you will build image compressor using singular value decomposition, in the third project, you will predict real estate market using linear regression, in the fourth project, you will do text mining using non negative matrix factorization, and in the last project, you will perform dimensionality reduction using principal component analysis.First of all, before getting into the course, we need to ask ourselves this question, why should we learn about computational linear algebra? Well, here is my answer. Linear algebra serves as the foundation for many advanced mathematical concepts and techniques used in machine learning, data science, and engineering. In machine learning, linear algebra is essential for understanding and implementing algorithms such as linear regression, support vector machines, and neural networks. In data science, linear algebra enables us to analyze large datasets efficiently, perform dimensionality reduction, and solve optimization problems. In engineering, linear algebra plays a critical role in modeling physical systems, designing control systems, and solving differential equations.Below are things that you can expect to learn from this course:Learn the basic fundamentals of linear algebra, such as getting to know its real world applications and important key conceptsLearn about the difference between scalar, vector, matrix, and tensorLearn how to add and subtract matrix using NumpyLearn how to multiply matrix using NumpyLearn how to inverse and transpose matrix using NumpyLearn how to calculate matrix determinant using NumpyLearn how to calculate matrix norm, trace, and rank using NumpyLearn how to solve system of linear equation using NumpyLearn how to calculate eigenvalues and eigenvectors using NumpyLearn about LU, QR, and Cholesky decompositionLearn how to create, slice, and reshape tensor using NumpyLearn how to build movie recommendation engine using linear decompositionLearn how to build image compressor using singular value decompositionLearn how to predict real estate market using linear regressionLearn how to do text mining using non negative matrix factorizationLearn how to perform dimensionality reduction using principal component analysis
