Free Course Image Linear algebra

Free online courseLinear algebra

Duration of the online course: 27 hours and 55 minutes

4.91

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(120)

Explore Linear Algebra through a comprehensive free online course covering 34 lectures from MIT’s Spring 2005 series. Perfect for beginners in Algebra.

In this free course, learn about

  • Systems of Linear Equations and Matrices
  • Subspaces, Rank, and the Four Fundamental Subspaces
  • Orthogonality, Projections, and Least Squares
  • Determinants and Their Properties
  • Eigenvalues, Eigenvectors, and Diagonalization
  • Markov Matrices, Invertibility, and Symmetric Matrices
  • Fourier Methods and Positive Definite Matrices
  • Similarity, SVD, and Linear Transformations
  • Applications: Image Representation and Advanced Topics

Course Description

Linear Algebra is an engaging and comprehensive course that spans 27 hours and 55 minutes of content. It firmly establishes itself within the Basic Studies category, specifically under the subcategory of Algebra. The course has garnered significant acclaim, reflected in its outstanding average rating of 4.91 out of 5 stars.

Designed for learners interested in delving into the fundamentals of Linear Algebra, the course draws from the esteemed lectures of MIT’s 18.06 Linear Algebra, Spring 2005. Each lecture, skillfully delivered, progressively builds on essential concepts, ensuring a structured and thorough learning experience for students.

The course covers a wide array of topics vital to understanding linear algebra. Starting with introductory concepts and moving through various essential elements and applications of linear algebra, each lecture meticulously unpacks the theories and practices that form the backbone of this mathematical discipline. Learners will find themselves immersed in a methodical exploration of topics, from basic vector and matrix operations to more advanced concepts like eigenvalues and eigenvectors.

What sets this course apart is its methodical approach to complex topics. The lecturer breaks down intricate concepts into manageable segments, making them accessible to learners at all levels. Whether you are just beginning your journey in linear algebra or seeking to solidify and expand your understanding, you will find the course material both challenging and rewarding.

Each lecture builds on the previous one, reinforcing and expanding on the knowledge acquired. Students are engaged through a series of intuitive and insightful explanations, which are supplemented by practical examples and problem-solving exercises. The course promotes not just rote learning but also a deeper understanding of the underlying principles and real-world applications of linear algebra.

In addition to the rich content and exemplary teaching methods, the course has been meticulously curated to ensure clarity and coherence. Whether it is the clear exposition of matrix theory or the step-by-step breakdown of vector spaces, each topic is delivered with precision and pedagogy that reflect the dedication to education and MIT's commitment to excellence.

Overall, Linear Algebra is an invaluable resource for anyone looking to gain a robust understanding of linear algebra. Its high rating emphasizes the positive reception by students who have found the course to be educational, insightful, and highly beneficial. This course stands as a testament to effective teaching and well-organized content, making it an ideal choice for learners aiming to excel in the field of algebra.

Course content

  • Video class: Lec 1 | MIT 18.06 Linear Algebra, Spring 2005 39m
  • Exercise: What is the point of origin in a line?
  • Video class: Lec 2 | MIT 18.06 Linear Algebra, Spring 2005 47m
  • Exercise: Which method is primarily used to solve systems of equations in the lecture?
  • Video class: Lec 3 | MIT 18.06 Linear Algebra, Spring 2005 46m
  • Exercise: What is the essential requirement for matrix multiplication?
  • Video class: Lec 4 | MIT 18.06 Linear Algebra, Spring 2005 50m
  • Exercise: What is the inverse of the product of two invertible matrices A and B?
  • Video class: Lec 5 | MIT 18.06 Linear Algebra, Spring 2005 47m
  • Exercise: What determines if a matrix operation requires row exchanges?
  • Video class: Lec 6 | MIT 18.06 Linear Algebra, Spring 2005 46m
  • Exercise: Can the union of two subspaces form another subspace?
  • Video class: Lec 7 | MIT 18.06 Linear Algebra, Spring 2005 43m
  • Exercise: What is the rank of a matrix in linear algebra?
  • Video class: Lec 8 | MIT 18.06 Linear Algebra, Spring 2005 47m
  • Exercise: What is the solution of AX=B in class eight?
  • Video class: Lec 9 | MIT 18.06 Linear Algebra, Spring 2005 50m
  • Exercise: What determines if a set of vectors are independent?
  • Video class: Lec 10 | MIT 18.06 Linear Algebra, Spring 2005 49m
  • Exercise: What is the fourth fundamental subspace in linear algebra?
  • Video class: Lec 11 | MIT 18.06 Linear Algebra, Spring 2005 45m
  • Exercise: What is the dimension of the subspace of three by three symmetric matrices?
  • Video class: Lec 12 | MIT 18.06 Linear Algebra, Spring 2005 47m
  • Exercise: What is the rank of the incidence matrix from the graph in the example?
  • Video class: Lec 13 | MIT 18.06 Linear Algebra, Spring 2005 47m
  • Exercise: Determine the possible dimensions of the subspace spanned by u, v, and w in R^7
  • Video class: Lec 14 | MIT 18.06 Linear Algebra, Spring 2005 49m
  • Exercise: What is the angle between 2 orthogonal subspaces?
  • Video class: Lec 15 | MIT 18.06 Linear Algebra, Spring 2005 48m
  • Exercise: What happens to the projection if vector 'b' is doubled?
  • Video class: Lec 16 | MIT 18.06 Linear Algebra, Spring 2005 48m
  • Exercise: What does the projection matrix P do when vector b is in the column space?
  • Video class: Lec 17 | MIT 18.06 Linear Algebra, Spring 2005 49m
  • Exercise: What property does a matrix with orthonormal columns have when multiplied by its transpose?
  • Video class: Lec 18 | MIT 18.06 Linear Algebra, Spring 2005 49m
  • Exercise: What is the determinant of a square matrix used for?
  • Video class: Lec 19 | MIT 18.06 Linear Algebra, Spring 2005 53m
  • Exercise: What is the determinant of a 2x2 matrix with elements a, b, c, d?
  • Video class: Lec 20 | MIT 18.06 Linear Algebra, Spring 2005 51m
  • Exercise: What is a property of the determinant used in finding the inverse of a matrix?
  • Video class: Lec 21 | MIT 18.06 Linear Algebra, Spring 2005 51m
  • Exercise: What is an eigenvector?
  • Video class: Lec 22 | MIT 18.06 Linear Algebra, Spring 2005 51m
  • Exercise: What is the condition for diagonalizing a matrix?
  • Video class: Lec 23 | MIT 18.06 Linear Algebra, Spring 2005 51m
  • Exercise: What is the significance of eigenvalues in solving differential equations?
  • Video class: Lec 24 | MIT 18.06 Linear Algebra, Spring 2005 51m
  • Exercise: What is a key property of Markov matrices?
  • Video class: Lec 24b | MIT 18.06 Linear Algebra, Spring 2005 48m
  • Exercise: What is the condition for a matrix to be invertible?
  • Video class: Lec 25 | MIT 18.06 Linear Algebra, Spring 2005 43m
  • Exercise: What is a characteristic of symmetric matrices that affects their eigenvalues and eigenvectors?
  • Video class: Lec 26 | MIT 18.06 Linear Algebra, Spring 2005 47m
  • Exercise: What is one key benefit of the Fast Fourier Transform (FFT)?
  • Video class: Lec 27 | MIT 18.06 Linear Algebra, Spring 2005 50m
  • Exercise: How can you determine if a matrix is positive definite?
  • Video class: Lec 28 | MIT 18.06 Linear Algebra, Spring 2005 45m
  • Exercise: What does it mean for two matrices to be similar?
  • Video class: Lec 29 | MIT 18.06 Linear Algebra, Spring 2005 41m
  • Exercise: What is the structure of the Singular Value Decomposition (SVD)?
  • Video class: Lec 30 | MIT 18.06 Linear Algebra, Spring 2005 49m
  • Exercise: What is a linear transformation?
  • Video class: Lec 31 | MIT 18.06 Linear Algebra, Spring 2005 50m
  • Exercise: What is a pixel?
  • Video class: Lec 32 | MIT 18.06 Linear Algebra, Spring 2005 47m
  • Exercise: What is special about eigenvalues of symmetric matrices?
  • Video class: Lec 33 | MIT 18.06 Linear Algebra, Spring 2005 41m
  • Exercise: What happens to the rank of a matrix when it is invertible?
  • Video class: Lec 34 | MIT 18.06 Linear Algebra, Spring 2005 43m
  • Exercise: What Characteristic of the Matrix A Ensures A Transpose A is Invertible?

This free course includes:

27 hours and 55 minutes of online video course

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Exercises to train your knowledge

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