# An Introduction to Matrix Lie Groups

- Institution: IISER Mohali
- Department: Mathematics
- Teacher: Prof. Krishnendu Gongopadhyay
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106904)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106904)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Complex Numbers](https://invisiblenetwork.ai/learn/nptel/111106904/c32d3ebf4a82) (Video)
2. [The Plane Rotations](https://invisiblenetwork.ai/learn/nptel/111106904/eef9e3d1a656) (Video)
3. [The Quaternions](https://invisiblenetwork.ai/learn/nptel/111106904/276b20860ba8) (Video)
4. [Quaternionic matrices](https://invisiblenetwork.ai/learn/nptel/111106904/588fcadecdf0) (Video)
5. [What is a Matrix Lie Group](https://invisiblenetwork.ai/learn/nptel/111106904/a6aa04881c50) (Video)
6. [General Linear Group](https://invisiblenetwork.ai/learn/nptel/111106904/ae272065120f) (Video)
7. [Complex matrices as real matrices](https://invisiblenetwork.ai/learn/nptel/111106904/58ae6f3479e6) (Video)
8. [Quaternionic matrices as real matrices](https://invisiblenetwork.ai/learn/nptel/111106904/fcc6087c39e6) (Video)
9. [Discussions on quaternions](https://invisiblenetwork.ai/learn/nptel/111106904/189aa76922ec) (Video)
10. [Topology of matrix groups](https://invisiblenetwork.ai/learn/nptel/111106904/0ead3c0a00fc) (Video)
11. [Topology of matrix groups: Closedness](https://invisiblenetwork.ai/learn/nptel/111106904/1dec4a353071) (Video)
12. [Path-Connected subsets in R^m](https://invisiblenetwork.ai/learn/nptel/111106904/318e6a8ab3ed) (Video)
13. [Compactness in R^m](https://invisiblenetwork.ai/learn/nptel/111106904/56ceaf790375) (Video)
14. [Inner products](https://invisiblenetwork.ai/learn/nptel/111106904/2b7c05a28f7b) (Video)
15. [Unitary transformations](https://invisiblenetwork.ai/learn/nptel/111106904/0931409fa954) (Video)
16. [Unitary matrices](https://invisiblenetwork.ai/learn/nptel/111106904/766b6e861449) (Video)
17. [Congruence](https://invisiblenetwork.ai/learn/nptel/111106904/5e98c4c51044) (Video)
18. [Euclidean isometries](https://invisiblenetwork.ai/learn/nptel/111106904/21d96f1a7906) (Video)
19. [Two dimensional Euclidean Isometries](https://invisiblenetwork.ai/learn/nptel/111106904/7bfbebf4ce02) (Video)
20. [Compactness of unitary groups](https://invisiblenetwork.ai/learn/nptel/111106904/258237e7d3c6) (Video)
21. [Connectedness of complex matrix groups](https://invisiblenetwork.ai/learn/nptel/111106904/66ddd53bf34d) (Video)
22. [Connectedness of real matrix groups](https://invisiblenetwork.ai/learn/nptel/111106904/ab85e0827ad5) (Video)
23. [Differentiability of a function](https://invisiblenetwork.ai/learn/nptel/111106904/096fd38f3536) (Video)
24. [Differentiability of a function-II](https://invisiblenetwork.ai/learn/nptel/111106904/2aae2e08682f) (Video)
25. [What is a Lie Algebra](https://invisiblenetwork.ai/learn/nptel/111106904/490885a6e2e7) (Video)
26. [Examples of Lie algebras](https://invisiblenetwork.ai/learn/nptel/111106904/5f1b1898059f) (Video)
27. [Lie algebra for special linear groups](https://invisiblenetwork.ai/learn/nptel/111106904/f260a5309335) (Video)
28. [Lie algebra as vector fields](https://invisiblenetwork.ai/learn/nptel/111106904/f8499af28e50) (Video)
29. [Lie algebras for orthogonal and unitary groups](https://invisiblenetwork.ai/learn/nptel/111106904/4233a09e171c) (Video)
30. [Series of Matrices](https://invisiblenetwork.ai/learn/nptel/111106904/76fc38e27643) (Video)
31. [Series of Matrices](https://invisiblenetwork.ai/learn/nptel/111106904/820da60913c7) (Video)
32. [Exponential map](https://invisiblenetwork.ai/learn/nptel/111106904/d24613d02189) (Video)
33. [Properties of Exponential Map](https://invisiblenetwork.ai/learn/nptel/111106904/4b90ec670cfa) (Video)
34. [One parameter Subgroups](https://invisiblenetwork.ai/learn/nptel/111106904/3f8eeddc0f83) (Video)
35. [Matrix logarithm](https://invisiblenetwork.ai/learn/nptel/111106904/43544c26b294) (Video)
36. [Inverse Function Theorem](https://invisiblenetwork.ai/learn/nptel/111106904/57733b2255e2) (Video)
37. [Image of the Exponential map.](https://invisiblenetwork.ai/learn/nptel/111106904/e35e625c6d32) (Video)
38. [Exponential map is a local diffeomorphism](https://invisiblenetwork.ai/learn/nptel/111106904/1ab3a9ff8c5c) (Video)
39. [Every matrix group is a manifold](https://invisiblenetwork.ai/learn/nptel/111106904/8e03aa133cb3) (Video)
40. [Calculus on Manifolds](https://invisiblenetwork.ai/learn/nptel/111106904/61cecb6b35ea) (Video)
41. [The Lie Bracket](https://invisiblenetwork.ai/learn/nptel/111106904/5921dc880727) (Video)
42. [Lie Algebra isomorphisms and Matrix Group isomorphisms](https://invisiblenetwork.ai/learn/nptel/111106904/81dcde8aac2c) (Video)
43. [Example of isomorphic Lie algebras](https://invisiblenetwork.ai/learn/nptel/111106904/e89e458cac2d) (Video)
44. [The adjoint Representation](https://invisiblenetwork.ai/learn/nptel/111106904/bf13d31b9adc) (Video)
45. [Adjoint representation for compact matrix groups](https://invisiblenetwork.ai/learn/nptel/111106904/ced5d4b75a5b) (Video)
46. [Shape of space rotations](https://invisiblenetwork.ai/learn/nptel/111106904/394cad32a3ad) (Video)
47. [More double covers](https://invisiblenetwork.ai/learn/nptel/111106904/7697f75ccca1) (Video)
48. [More double covers-II](https://invisiblenetwork.ai/learn/nptel/111106904/e1a4591b62b7) (Video)
49. [Overview of Simply Connectedness](https://invisiblenetwork.ai/learn/nptel/111106904/7884ebf22e8b) (Video)
50. [Correspondence between connected subgroups and Lie Ideals](https://invisiblenetwork.ai/learn/nptel/111106904/888846f53480) (Video)
51. [Discrete subgroups - I](https://invisiblenetwork.ai/learn/nptel/111106904/98469034f32b) (Video)
52. [Discrete subgroups - II](https://invisiblenetwork.ai/learn/nptel/111106904/57faf736579e) (Video)
53. [Characterization of Torus](https://invisiblenetwork.ai/learn/nptel/111106904/c494d780702e) (Video)
54. [Maximal Torus](https://invisiblenetwork.ai/learn/nptel/111106904/d419a5998069) (Video)
55. [Non-compact Examples: Lorentzian groups](https://invisiblenetwork.ai/learn/nptel/111106904/4d48df85b2d8) (Video)
56. [Symplectic groups](https://invisiblenetwork.ai/learn/nptel/111106904/1beb35edc54c) (Video)
57. [Introduction to Smooth Manifolds](https://invisiblenetwork.ai/learn/nptel/111106904/0f9828982dd0) (Video)
58. [Tangent spaces to Smooth Manifolds](https://invisiblenetwork.ai/learn/nptel/111106904/089bdf19df6c) (Video)
59. [Lie groups](https://invisiblenetwork.ai/learn/nptel/111106904/0b276b49a979) (Video)