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Open CosmologyPhysics & cosmology: four years, plus a graduate year
Mathematics · Year II

18.06 Linear Algebra

Systems of linear equations, matrices, vector spaces, orthogonality, determinants, eigenvalues and eigenvectors, positive definite matrices and the singular value decomposition.

Based on MIT OpenCourseWare, Spring 2010 · Prof. Gilbert Strang · Course on OCW

Lectures (0 of 35 with pages so far)

  1. Lecture 1The geometry of linear equationsMIT ↗
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  2. Lecture 2Elimination with matricesMIT ↗
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  3. Lecture 3Multiplication and inverse matricesMIT ↗
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  4. Lecture 4Factorization into A = LUMIT ↗
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  5. Lecture 5Transposes, permutations, spaces R^nMIT ↗
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  6. Lecture 6Column space and nullspaceMIT ↗
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  7. Lecture 7Solving Ax = 0: pivot variables, special solutionsMIT ↗
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  8. Lecture 8Solving Ax = b: row reduced form RMIT ↗
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  9. Lecture 9Independence, basis, and dimensionMIT ↗
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  10. Lecture 10The four fundamental subspacesMIT ↗
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  11. Lecture 11Matrix spaces; rank 1; small world graphsMIT ↗
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  12. Lecture 12Graphs, networks, incidence matricesMIT ↗
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  13. Lecture 13Quiz 1 reviewMIT ↗
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  14. Lecture 14Orthogonal vectors and subspacesMIT ↗
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  15. Lecture 15Projections onto subspacesMIT ↗
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  16. Lecture 16Projection matrices and least squaresMIT ↗
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  17. Lecture 17Orthogonal matrices and Gram-SchmidtMIT ↗
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  18. Lecture 18Properties of determinantsMIT ↗
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  19. Lecture 19Determinant formulas and cofactorsMIT ↗
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  20. Lecture 20Cramer's rule, inverse matrix, and volumeMIT ↗
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  21. Lecture 21Eigenvalues and eigenvectorsMIT ↗
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  22. Lecture 22Diagonalization and powers of AMIT ↗
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  23. Lecture 23Differential equations and exp(At)MIT ↗
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  24. Lecture 24Markov matrices; fourier seriesMIT ↗
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  25. Lecture 24bQuiz 2 reviewMIT ↗
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  26. Lecture 25Symmetric matrices and positive definitenessMIT ↗
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  27. Lecture 26Complex matrices; fast fourier transformMIT ↗
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  28. Lecture 27Positive definite matrices and minimaMIT ↗
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  29. Lecture 28Similar matrices and Jordan formMIT ↗
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  30. Lecture 29Singular value decompositionMIT ↗
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  31. Lecture 30Linear transformations and their matricesMIT ↗
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  32. Lecture 31Change of basis; image compressionMIT ↗
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  33. Lecture 32Quiz 3 reviewMIT ↗
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  34. Lecture 33Left and right inverses; pseudoinverseMIT ↗
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  35. Lecture 34Final course reviewMIT ↗
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