This video will introduce the orthogonal groups, with the simplest example of SO(2). I will discuss how the group manifold should be realised as topologically equivalent to the circle S^1, to start building intuition about the geometric significance of Lie groups (as manifolds).
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Lie Groups #2 - The orthogonal group SO(2)
Теги
MathsMathPhysicsTensorVectorAlgebraAbstract AlgebraAlgebraic StructureGroupDifferential GeometryLinear AlgebraMultilinear AlgebraUndergraduateEducationTopologyTopological SpacesManifoldsContinuityMapsSetsCircleTorusS^1AbstractSetEquivalence RelationGaugeGauge theoryEinstein Cartan theoryEdge modesEinsteinCartanBoundaryBoundary conditionHomotopyPullbackCategoryGroupoidLie groupRotationOrthogonalSO(2)
