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An Introduction to Matrix Lie Groups TY2KERW0XE

URIm2://res/TY2KERW0XE
Kindcourse
CreatorsKrishnendu Gongopadhyay (instructor)
Date2026-09-04
Scopein

Expressions

e1: edition

Languageen
Date2026-09-04
Contents
  • part 1: Week 1
  • session 1: Complex Numbers
  • session 2: The Plane Rotations
  • session 3: The Quaternions
  • session 4: Quaternionic matrices
  • part 2: Week 2
  • session 5: What is a Matrix Lie Group
  • session 6: General Linear Group
  • session 7: Complex matrices as real matrices
  • session 8: Quaternionic matrices as real matrices
  • session 9: Discussions on quaternions
  • part 3: Week 3
  • session 10: Topology of matrix groups
  • session 11: Topology of matrix groups: Closedness
  • session 12: Path-Connected subsets in R^m
  • session 13: Compactness in R^m
  • part 4: Week 4
  • session 14: Inner products
  • session 15: Unitary transformations
  • session 16: Unitary matrices
  • session 17: Congruence
  • session 18: Euclidean isometries
  • session 19: Two dimensional Euclidean Isometries
  • part 5: Week 5
  • session 20: Compactness of unitary groups
  • session 21: Connectedness of complex matrix groups
  • session 22: Connectedness of real matrix groups
  • session 23: Differentiability of a function
  • session 24: Differentiability of a function-II
  • part 6: Week 6
  • session 25: What is a Lie Algebra
  • session 26: Examples of Lie algebras
  • session 27: Lie algebra for special linear groups
  • session 28: Lie algebra as vector fields
  • session 29: Lie algebras for orthogonal and unitary groups
  • part 7: Week 7
  • session 30: Series of Matrices
  • session 31: Series of Matrices
  • session 32: Exponential map
  • session 33: Properties of Exponential Map
  • session 34: One parameter Subgroups
  • session 35: Matrix logarithm
  • part 8: Week 8
  • session 36: Inverse Function Theorem
  • session 37: Image of the Exponential map.
  • session 38: Exponential map is a local diffeomorphism
  • session 39: Every matrix group is a manifold
  • session 40: Calculus on Manifolds
  • part 9: Week 9
  • session 41: The Lie Bracket
  • session 42: Lie Algebra isomorphisms and Matrix Group isomorphisms
  • session 43: Example of isomorphic Lie algebras
  • session 44: The adjoint Representation
  • session 45: Adjoint representation for compact matrix groups
  • part 10: Week 10
  • session 46: Shape of space rotations
  • session 47: More double covers
  • session 48: More double covers-II
  • session 49: Overview of Simply Connectedness
  • session 50: Correspondence between connected subgroups and Lie Ideals
  • part 11: Week 11
  • session 51: Discrete subgroups - I
  • session 52: Discrete subgroups - II
  • session 53: Characterization of Torus
  • session 54: Maximal Torus
  • part 12: Week 12
  • session 55: Non-compact Examples: Lorentzian groups
  • session 56: Symplectic groups
  • session 57: Introduction to Smooth Manifolds
  • session 58: Tangent spaces to Smooth Manifolds
  • session 59: Lie groups

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