内容简介：Gilbert Strang.For more information about using these materials and the Creative Commons license, see ourTerms of Use.
A 2020 Vision of Linear Algebra
Professor Strang introduces his new vision of how to teach linear algebra. (Image by MIT OCW)
Instructor(s)
Prof. Gilbert Strang
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Course Description
These six 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 .
You can see this new idea developing in thefirst video lecture of Professor Strang’s 2019 course 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning .
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Gilbert Strang. RES.18-010 A 2020 Vision of Linear Algebra. Spring 2020. Massachusetts Institute of Technology: MIT OpenCourseWare,https://ocw.mit.edu. License: Creative Commons BY-NC-SA .
For more information about using these materials and the Creative Commons license, see ourTerms of Use.
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