Essential Linear Algebra for Data Science
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Essential Linear Algebra for Data Science
This course is part of Expressway to Data Science: Essential Math Specialization
Instructor: James Bird
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What you'll learn
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
Details to know
13 assignments
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There are 5 modules in this course
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.
This course is designed to prepare learners to successfully complete Statistical Modeling for Data Science Application, which is part of CU Boulder's Master of Science in Data Science (MS-DS) program. Logo courtesy of Dan-Cristian PΔdureΘ on Unsplash.com
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.
What's included
13 videos1 reading2 assignments
13 videosβ’Total 74 minutes
- Introduction to the Courseβ’1 minute
- Linear System and Definitionβ’3 minutes
- Three Solution Options and Coordinate System Visualizationβ’4 minutes
- Linear System -> Matrix (Coefficient and Augmented)β’5 minutes
- Rules of G.E. and Solving a Linear Systemβ’4 minutes
- G.E. Intuition and Simple Exampleβ’5 minutes
- G.E Example - Single Solution Part 1β’12 minutes
- G.E Example - Single Solution Part 2β’7 minutes
- G.E Example - Single Solution Part 3 + Meaningβ’3 minutes
- G.E. Example - Infinite Solutionsβ’4 minutes
- G.E. Example - No Solutionsβ’8 minutes
- G.E. Advanced Example - Part 1β’8 minutes
- G.E. Advanced Example - Part 2β’11 minutes
1 readingβ’Total 1 minute
- Course Updates and Accessibility Supportβ’1 minute
2 assignmentsβ’Total 15 minutes
- Practice - Linear System -> Matrix Formatβ’5 minutes
- LS -> Matrix + G.E. Full Question Quizβ’10 minutes
In this module we will learn how to solve a linear system of equations with matrix algebra.
What's included
6 videos2 assignments
6 videosβ’Total 35 minutes
- Matrix Algebra Sumβ’5 minutes
- Matrix Algebra Scale + Identity Overviewβ’4 minutes
- Matrix Multiplication + Small Exampleβ’9 minutes
- Matrix Multiplication - General Rulesβ’5 minutes
- Matrix Multiplication Exampleβ’6 minutes
- Identity Matrix + Exampleβ’7 minutes
2 assignmentsβ’Total 30 minutes
- Quiz on Matrix Algebra Sum + Scaleβ’15 minutes
- Matrix Multiplicationβ’15 minutes
In this module we will explore concepts and properties of linear systems. This includes independence, basis, rank, row space, column space, and much more.
What's included
15 videos3 assignments
15 videosβ’Total 87 minutes
- Introduction to Vectors + Coordinatesβ’7 minutes
- Introduction to Linear Combinationsβ’3 minutes
- Linear Combinationsβ’2 minutes
- Linear Combinations Exampleβ’10 minutes
- Spanβ’5 minutes
- Span Exampleβ’10 minutes
- Ax = bβ’8 minutes
- Linear Independenceβ’5 minutes
- Linear Independence Example Part 1β’8 minutes
- Linear Independence Example Part 2β’4 minutes
- Columns of a Matrix Being Linearly Independentβ’5 minutes
- Linear Transformationsβ’3 minutes
- Linear Transformations Exampleβ’4 minutes
- Matrix Inverseβ’4 minutes
- Matrix Inverse Exampleβ’8 minutes
3 assignmentsβ’Total 35 minutes
- Why do we use matrices and vectors and not just one?β’5 minutes
- Quiz on Linear Independenceβ’10 minutes
- Quiz on Transformations and Inverseβ’20 minutes
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.
What's included
8 videos3 assignments
8 videosβ’Total 51 minutes
- Determinant Intro and 2x2 Exampleβ’2 minutes
- Inverse of 2x2 Matrix - Quick Methodβ’5 minutes
- Determinant of 3x3 Matrix - Overviewβ’8 minutes
- Determinant of 3x3 Matrix - Example with 1st Rowβ’7 minutes
- Determinant of 3x3 Matrix - Example with 2nd Rowβ’8 minutes
- Eigenvalue and Eigenvector - Overviewβ’6 minutes
- Finding Eigenvector if Given Eigenvalueβ’9 minutes
- Characteristic Polynomic - Finding Eigenvaluesβ’7 minutes
3 assignmentsβ’Total 30 minutes
- Find the Determinant of a 2x2 Matrixβ’5 minutes
- Find Eigenvalue then Eigenvector of a Matrix (2x2)β’10 minutes
- Find Eigenvalue then Eigenvector of a Matrix (3x3)β’15 minutes
In this module we will learn how to compute the determinant of a matrix. Afterwards, Eigenvalues and Eigenvectors will be covered.
What's included
9 videos3 assignments
9 videosβ’Total 41 minutes
- Transpose and Inner (Dot) Productβ’7 minutes
- Norm (Length) of a Vectorβ’4 minutes
- Unit Vector Creationβ’4 minutes
- Distance Between Two Vectorsβ’3 minutes
- Orthogonal Vectorsβ’4 minutes
- Orthogonal Projections Part Iβ’5 minutes
- Orthogonal Projections Part IIβ’2 minutes
- Least Squares Overviewβ’5 minutes
- Least Squares Exampleβ’7 minutes
3 assignmentsβ’Total 70 minutes
- Important Final Conceptsβ’30 minutes
- Finding Least Squares Solutionsβ’10 minutes
- Final Examβ’30 minutes
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Reviewed on Feb 24, 2025
Nice concise explanations, but I feel like there are way too few practice problems. I ended up having to search online for additional resources to practice the concepts
Reviewed on May 14, 2023
Good course overall. Instructor explained the concepts really well.
Reviewed on May 9, 2022
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.
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