Linear Algebra Basics from Coursera

What's inside

Syllabus

Getting Started with the Course

This module provides an overview of the course content and structure. In this module, you will learn about the different course elements. In this module, you will get acquainted with your instructor and get an opportunity to introduce yourself and interact with your peers.

Vector Space

In this module, you will learn about vector space and its subspace. Further, you will learn about the set of linearly dependent and independent vectors. You will also gain insight into the linear combination and linear span of a set of vectors.

Linear Transformations and Eigenvalues

In this module, you will learn about the basis and dimension of a vector space. You will learn about the concept of linear transformations defined on real vector spaces. Further, you will understand that there is a matrix associated with each linear transformation for the bases. Finally, you will get an insight into the eigenvalues of a square matrix.

Diagonalizable Matrices and Their Applications

In this module, you will learn about the eigenvectors corresponding to the eigenvalues of a matrix. You will then learn about the properties of special matrices (symmetric and skew-symmetric). Finally, you will learn about the concept of diagonalization of a matrix (eigen decomposition of a matrix) with its applications.

Singular Value Decomposition of a Matrix and Inner Product of Vectors

In this module, you will learn about the spectral value decomposition and singular value decomposition of a matrix with some applications. Further, you will learn about the inner product space and norms of vectors and matrices with two useful identities—Cauchy-Schwarz inequality and Polarization identity—for machine learning algorithms.

Term-End Assignment

In this module, you are provided with your term-end project, instructions to complete the project, and the criteria for how your instructor will grade your submission.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Taught by Dr. S. K. Gupta, who is recognized for their work in the field of machine learning and data science

Builds a strong foundation for beginners in linear algebra, which is a core skill for machine learning and data science

Covers the mathematical concepts related to linear algebra, which include vector spaces, subspaces, linear span, basis, and dimension

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Linear Algebra Basics with these activities:

Review Basic Linear Algebra Concepts

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Refreshing basic linear algebra concepts can provide a foundation for understanding more advanced topics covered in the course.

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Review notes or textbooks on basic linear algebra
Solve practice problems to reinforce understanding

Review Matrix Operations

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Reviewing matrix operations can provide a foundation for understanding linear transformations and linear equations covered in the course.

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Identify different matrix operations, such as addition, subtraction, scalar multiplication, and matrix multiplication
Practice applying these operations to manipulate matrices

Join a Study Group for Linear Algebra Concepts

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Participating in a study group allows for collaborative learning, discussion of concepts, and support from peers, which can enhance understanding throughout the course.

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Find or create a study group with classmates
Meet regularly to discuss course material
Work together on practice problems and assignments

Five other activities

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Explore Tutorials on Eigenvalues and Eigenvectors

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Tutorials on eigenvalues and eigenvectors can provide additional insights and examples to enhance comprehension of this topic covered in Module 3.

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Search for tutorials on eigenvalues and eigenvectors
Follow the steps and examples provided in the tutorials
Try solving practice problems related to eigenvalues and eigenvectors

Develop a Presentation on Linear Transformations

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Creating a presentation on linear transformations provides an opportunity to synthesize knowledge, explain concepts, and improve communication skills covered in Module 2.

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Research and gather information on linear transformations
Organize the content into a logical flow
Design slides with clear and concise explanations
Practice presenting the material

Solve Practice Problems on Singular Value Decomposition

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Solving practice problems on singular value decomposition can reinforce understanding and improve problem-solving skills covered in Module 5.

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Find practice problems on singular value decomposition
Attempt to solve the problems using the concepts learned in the course
Review and correct your solutions against the provided answers or consult with others

Participate in Linear Algebra Competitions

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Participating in competitions can challenge understanding, foster problem-solving skills, and provide recognition for excellence in linear algebra, which is related to the topics covered in this course.

Browse courses on Linear Algebra

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Research and find suitable linear algebra competitions
Practice solving problems and prepare for the competition
Participate in the competition and strive for success

Contribute to Open-Source Projects on Linear Algebra

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Contributing to open-source projects allows for practical application of linear algebra concepts, exposure to real-world challenges, and collaboration with others in the field.

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Identify open-source projects related to linear algebra
Review the project documentation and codebase
Identify a suitable area to contribute
Submit a code contribution or issue report

Career center

Learners who complete Linear Algebra Basics will develop knowledge and skills that may be useful to these careers:

Data Scientist

Data Scientists use linear algebra to solve complex problems in various industries, including finance, healthcare, and manufacturing. This course can help build a foundation in linear algebra, which is essential for understanding and applying machine learning algorithms. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in data science.

See salaries and explore the career path for Data Scientist

Machine Learning Engineer

Machine Learning Engineers use linear algebra to develop and implement machine learning models. This course can help build a strong foundation in linear algebra, which is essential for understanding machine learning algorithms. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in machine learning.

See salaries and explore the career path for Machine Learning Engineer

Quantitative Analyst

Quantitative Analysts use linear algebra to model and analyze financial data. This course can help build a strong foundation in linear algebra, which is essential for understanding and applying quantitative analysis techniques. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in quantitative analysis.

See salaries and explore the career path for Quantitative Analyst

Actuary

Actuaries use linear algebra to model and analyze insurance and financial data. This course can help build a strong foundation in linear algebra, which is essential for understanding and applying actuarial techniques. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in actuarial science.

See salaries and explore the career path for Actuary

Financial Analyst

Financial Analysts use linear algebra to model and analyze financial data. This course can help build a strong foundation in linear algebra, which is essential for understanding and applying financial analysis techniques. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in financial analysis.

See salaries and explore the career path for Financial Analyst

Operations Research Analyst

Operations Research Analysts use linear algebra to optimize business processes. This course can help build a strong foundation in linear algebra, which is essential for understanding and applying operations research techniques. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in operations research.

See salaries and explore the career path for Operations Research Analyst

Software Engineer

Software Engineers use linear algebra to develop and implement software algorithms. This course may be useful for building a foundation in linear algebra, which can be helpful for understanding and applying software algorithms. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in software engineering.

See salaries and explore the career path for Software Engineer

Computer Scientist

Computer Scientists use linear algebra to develop and implement computer algorithms. This course may be useful for building a foundation in linear algebra, which can be helpful for understanding and applying computer algorithms. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in computer science.

See salaries and explore the career path for Computer Scientist

Mathematician

Mathematicians use linear algebra to solve complex mathematical problems. This course may be useful for building a foundation in linear algebra, which can be helpful for understanding and applying mathematical concepts. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in mathematics.

See salaries and explore the career path for Mathematician

Physicist

Physicists use linear algebra to model and analyze physical systems. This course may be useful for building a foundation in linear algebra, which can be helpful for understanding and applying physical concepts. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in physics.

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Economist

Economists use linear algebra to model and analyze economic systems. This course may be useful for building a foundation in linear algebra, which can be helpful for understanding and applying economic concepts. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in economics.

See salaries and explore the career path for Economist

Statistician

Statisticians use linear algebra to analyze data. This course may be useful for building a foundation in linear algebra, which can be helpful for understanding and applying statistical concepts. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in statistics.

See salaries and explore the career path for Statistician

Teacher

Teachers use linear algebra to teach mathematics and other subjects. This course may be useful for building a foundation in linear algebra, which can be helpful for understanding and teaching mathematical concepts. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in mathematics education.

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Consultant

Consultants use linear algebra to solve problems in various industries. This course may be useful for building a foundation in linear algebra, which can be helpful for understanding and applying consulting techniques. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in consulting.

See salaries and explore the career path for Consultant

Financial Advisor

Financial Advisors use linear algebra to manage and invest money. This course may be useful for building a foundation in linear algebra, which can be helpful for understanding and applying financial planning techniques. The course covers topics such as vector spaces, linear transformations, and eigenvalues, which are all fundamental concepts in financial planning.

See salaries and explore the career path for Financial Advisor