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Linear Algebra (MIT 18.06)

Gilbert Strang's complete course — elimination, subspaces, eigenvalues and the SVD

Taught by YouLearn Open Libraryلا مسجّلينحُدّثت في 24 غشت 2026
Linear Algebra (MIT 18.06)

عن هذه الدورة

The linear algebra course that taught a generation of engineers. Prof. Gilbert Strang starts from a system of two equations in two unknowns and builds, lecture by lecture, to the singular value decomposition — always asking what a matrix is doing geometrically before asking how to compute with it. Thirty-five recorded lectures from MIT, complete with the quiz reviews. Free to watch; the lecture videos stay on MIT OpenCourseWare and open in a new tab.

محتوى الدورة

7 أقسام · 35 درساً

  1. 1.Elimination and matrices

    8 دروس

    Solving a linear system by elimination, and the matrix factorisations that record what elimination did.

    • Lecture 1. The geometry of linear equationsSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010معاينة
    • Lecture 2. Elimination with matricesSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 3. Multiplication and inverse matricesSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 4. Factorization into A = LUSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 5. Transposes, permutations, spaces R^nSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 6. Column space and nullspaceSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 7. Solving Ax = 0: pivot variables, special solutionsSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 8. Solving Ax = b: row reduced form RSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010

  2. 2.Vector spaces and subspaces

    5 دروس

    The four fundamental subspaces, and what independence, basis and dimension actually mean.

    • Lecture 9. Independence, basis, and dimensionSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 10. The four fundamental subspacesSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 11. Matrix spaces; rank 1; small world graphsSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 12. Graphs, networks, incidence matricesSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 13. Quiz 1 reviewSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010

  3. 3.Orthogonality

    4 دروس

    Projection, least squares and Gram-Schmidt — the geometry behind fitting a line to data.

    • Lecture 14. Orthogonal vectors and subspacesSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 15. Projections onto subspacesSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 16. Projection matrices and least squaresSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 17. Orthogonal matrices and Gram-SchmidtSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010

  4. 4.Determinants

    3 دروس

    Three properties that define the determinant, and the formulas that follow from them.

    • Lecture 18. Properties of determinantsSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 19. Determinant formulas and cofactorsSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 20. Cramer's rule, inverse matrix, and volumeSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010

  5. 5.Eigenvalues and eigenvectors

    5 دروس

    Diagonalisation, powers of a matrix, differential equations and Markov chains.

    • Lecture 21. Eigenvalues and eigenvectorsSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 22. Diagonalization and powers of ASource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 23. Differential equations and exp(At)Source: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 24. Markov matrices; Fourier seriesSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 25. Quiz 2 reviewSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010

  6. 6.Symmetric and positive definite matrices

    4 دروس

    The best-behaved matrices there are, plus complex matrices and the FFT.

    • Lecture 26. Symmetric matrices and positive definitenessSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 27. Complex matrices; fast Fourier transformSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 28. Positive definite matrices and minimaSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 29. Similar matrices and Jordan formSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010

  7. 7.The SVD and linear transformations

    6 دروس

    Singular value decomposition, change of basis, and the pseudoinverse.

    • Lecture 30. Singular value decompositionSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 31. Linear transformations and their matricesSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 32. Change of basis; image compressionSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 33. Quiz 3 reviewSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 34. Left and right inverses; pseudoinverseSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010
    • Lecture 35. Final course reviewSource: MIT OpenCourseWare — 18.06 Linear Algebra, Spring 2010

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