Definition

Tangent Space

Lie Groups and Lie Algebras · lie-groups.tex

For $p \in M$ a smooth manifold (Definition~Smooth Manifold), the tangent space $T_pM$ is the vector space of derivations on smooth functions near $p$. Concretely in a chart, it is spanned by $\partial/\partial x^i|_p$. The tangent bundle is $TM = \bigsqcup_{p \in M} T_pM$.

Depends on

Smooth Manifold

Used in

Immersion and Embedding

Dependency Graph

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