Learn · An Introduction to Matrix Lie Groups

Lecture 24 of 59Week 5

Differentiability of a function-II

Prof. Krishnendu Gongopadhyay · IISER Mohali

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An Introduction to Matrix Lie Groups, IISER Mohali (at NPTEL)
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
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All the lectures

  1. Complex Numbers Video
  2. The Plane Rotations Video
  3. The Quaternions Video
  4. Quaternionic matrices Video
  5. What is a Matrix Lie Group Video
  6. General Linear Group Video
  7. Complex matrices as real matrices Video
  8. Quaternionic matrices as real matrices Video
  9. Discussions on quaternions Video
  10. Topology of matrix groups Video
  11. Topology of matrix groups: Closedness Video
  12. Path-Connected subsets in R^m Video
  13. Compactness in R^m Video
  14. Inner products Video
  15. Unitary transformations Video
  16. Unitary matrices Video
  17. Congruence Video
  18. Euclidean isometries Video
  19. Two dimensional Euclidean Isometries Video
  20. Compactness of unitary groups Video
  21. Connectedness of complex matrix groups Video
  22. Connectedness of real matrix groups Video
  23. Differentiability of a function Video
  24. Differentiability of a function-II Video
  25. What is a Lie Algebra Video
  26. Examples of Lie algebras Video
  27. Lie algebra for special linear groups Video
  28. Lie algebra as vector fields Video
  29. Lie algebras for orthogonal and unitary groups Video
  30. Series of Matrices Video
  31. Series of Matrices Video
  32. Exponential map Video
  33. Properties of Exponential Map Video
  34. One parameter Subgroups Video
  35. Matrix logarithm Video
  36. Inverse Function Theorem Video
  37. Image of the Exponential map. Video
  38. Exponential map is a local diffeomorphism Video
  39. Every matrix group is a manifold Video
  40. Calculus on Manifolds Video
  41. The Lie Bracket Video
  42. Lie Algebra isomorphisms and Matrix Group isomorphisms Video
  43. Example of isomorphic Lie algebras Video
  44. The adjoint Representation Video
  45. Adjoint representation for compact matrix groups Video
  46. Shape of space rotations Video
  47. More double covers Video
  48. More double covers-II Video
  49. Overview of Simply Connectedness Video
  50. Correspondence between connected subgroups and Lie Ideals Video
  51. Discrete subgroups - I Video
  52. Discrete subgroups - II Video
  53. Characterization of Torus Video
  54. Maximal Torus Video
  55. Non-compact Examples: Lorentzian groups Video
  56. Symplectic groups Video
  57. Introduction to Smooth Manifolds Video
  58. Tangent spaces to Smooth Manifolds Video
  59. Lie groups Video