These brief videos, recorded in 2020, contain ideas and suggestions from Professor Strang about the recommended order of topics in teaching and learning linear algebra. The first topic is called _A New Way to Start Linear Algebra_. The key point is to start right in with the columns of a matrix _A_ and the multiplication _Ax_ that combines those columns. That leads to _The Column Space of a Matrix_ and the idea of independent columns and the factorization _A = CR_ that tells so much about _A_. With good numbers, every student can see dependent columns. The remaining videos outline very briefly the full course: _The Big Picture of Linear Algebra_; _Orthogonal Vectors_; _Eigenvalues & Eigenvectors_; and _Singular Values & Singular Vectors_. Singular values have become so important and they come directly from the eigenvalues of _A'A_. A new video recorded in 2021, _Finding the Nullspace: Solving Ax = 0 by Elimination_, computes the nullspace of any matrix _A_. You can see this new idea developing in the [first video lecture](/courses/18-065-matrix-methods-in-data-analysis-signal-processing-and-machine-learning-spring-2018/resources/lecture-1-the-column-space-of-a-contains-all-vectors-ax) of Professor Strang’s 2019 course _[18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning](/courses/18-065-matrix-methods-in-data-analysis-signal-processing-and-machine-learning-spring-2018/)_.

MIT OpenCourseWare is a web based publication of virtually all MIT course content. OCW is open and available to the world and is a permanent MIT activity

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