Essential Linear Algebra for Data Science

Essential Linear Algebra for Data Science

本课程是 Expressway to Data Science: Essential Math 专项课程的一部分

位教师：James Bird

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5个模块

深入了解一个主题并学习基础知识。

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您将学到什么

Solve real-world problems using the foundational concept of matrices and explain where those problems might arise.
Recognize what a matrix represents in n-dimensional space and how transformations act in that space
Identify key properties of any system of equations, such as independence, basis, rank, and more, and what they mean for the overall system.
Demonstrate your understanding of projections in lower dimensions, while being able to carry out higher dimension projections for real-world problems

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作业

13 项作业

授课语言：英语（English）

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本课程是 Expressway to Data Science: Essential Math 专项课程专项课程的一部分

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该课程共有5个模块

Are you interested in Data Science but lack the math background for it? Has math always been a tough subject that you tend to avoid? This course will teach you the most fundamental Linear Algebra that you will need for a career in Data Science without a ton of unnecessary proofs and concepts that you may never use. Consider this an expressway to Data Science with approachable methods and friendly concepts that will guide you to truly understanding the most important ideas in Linear Algebra.

In this module we will learn what a matrix is and what it represents. We will explore how a system of linear equations can be expressed in a neat package via matrices. Lastly, we will delve into coordinate systems and provide visualizations to help you understand matrices in a more well-rounded way.

涵盖的内容

13个视频1篇阅读材料2个作业

13个视频总计74分钟

Introduction to the Course1分钟
Linear System and Definition3分钟
Three Solution Options and Coordinate System Visualization4分钟
Linear System -> Matrix (Coefficient and Augmented)5分钟
Rules of G.E. and Solving a Linear System4分钟
G.E. Intuition and Simple Example5分钟
G.E Example - Single Solution Part 112分钟
G.E Example - Single Solution Part 27分钟
G.E Example - Single Solution Part 3 + Meaning3分钟
G.E. Example - Infinite Solutions4分钟
G.E. Example - No Solutions8分钟
G.E. Advanced Example - Part 18分钟
G.E. Advanced Example - Part 211分钟

1篇阅读材料总计1分钟

Course Updates and Accessibility Support1分钟

2个作业总计15分钟

Practice - Linear System -> Matrix Format5分钟
LS -> Matrix + G.E. Full Question Quiz10分钟

In this module we will learn how to solve a linear system of equations with matrix algebra.

涵盖的内容

6个视频2个作业

In this module we will explore concepts and properties of linear systems. This includes independence, basis, rank, row space, column space, and much more.

涵盖的内容

15个视频3个作业

15个视频总计87分钟

Introduction to Vectors + Coordinates7分钟
Introduction to Linear Combinations3分钟
Linear Combinations2分钟
Linear Combinations Example10分钟
Span5分钟
Span Example10分钟
Ax = b8分钟
Linear Independence5分钟
Linear Independence Example Part 18分钟
Linear Independence Example Part 24分钟
Columns of a Matrix Being Linearly Independent5分钟
Linear Transformations3分钟
Linear Transformations Example4分钟
Matrix Inverse4分钟
Matrix Inverse Example8分钟

3个作业总计35分钟

Why do we use matrices and vectors and not just one?5分钟
Quiz on Linear Independence10分钟
Quiz on Transformations and Inverse20分钟

In this module we will discuss projections and how they work. We will build on a foundation using 2-dimensional projections and explore the concept in higher dimensions over time.

涵盖的内容

8个视频3个作业

8个视频总计51分钟

Determinant Intro and 2x2 Example2分钟
Inverse of 2x2 Matrix - Quick Method5分钟
Determinant of 3x3 Matrix - Overview8分钟
Determinant of 3x3 Matrix - Example with 1st Row7分钟
Determinant of 3x3 Matrix - Example with 2nd Row8分钟
Eigenvalue and Eigenvector - Overview6分钟
Finding Eigenvector if Given Eigenvalue9分钟
Characteristic Polynomic - Finding Eigenvalues7分钟

3个作业总计30分钟

Find the Determinant of a 2x2 Matrix5分钟
Find Eigenvalue then Eigenvector of a Matrix (2x2)10分钟
Find Eigenvalue then Eigenvector of a Matrix (3x3)15分钟

In this module we will learn how to compute the determinant of a matrix. Afterwards, Eigenvalues and Eigenvectors will be covered.

涵盖的内容

9个视频3个作业

9个视频总计41分钟

Transpose and Inner (Dot) Product7分钟
Norm (Length) of a Vector4分钟
Unit Vector Creation4分钟
Distance Between Two Vectors3分钟
Orthogonal Vectors4分钟
Orthogonal Projections Part I5分钟
Orthogonal Projections Part II2分钟
Least Squares Overview5分钟
Least Squares Example7分钟

3个作业总计70分钟

Important Final Concepts30分钟
Finding Least Squares Solutions10分钟
Final Exam30分钟

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位教师

授课教师评分

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James Bird

University of Colorado Boulder

3 门课程18,315 名学生

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University of Colorado Boulder

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学生评论

5 stars
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4 stars
10%
3 stars
6.84%
2 stars
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1 star
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已于 May 14, 2023审阅

Good course overall. Instructor explained the concepts really well.

已于 May 9, 2022审阅

Well-explained and comprehensive. I thought it was going to be a rough course but Professor Bird is very thorough and concise in his lectures.

已于 May 22, 2023审阅

Great professor. Easy to follow and exercises are good enough.

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