Linear Algebra: Multilinear Forms

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Explores multilinear forms in linear algebra, emphasizing their properties and applications.

Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Covers the concept of tensor product in the context of bilinear maps and explores the uniqueness of tensor products.

Covers the theory and applications of bilinear forms in various mathematical contexts.

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Explores symplectic groups, linear transformations preserving non-degenerate alternating bilinear forms on vector spaces.

Explores multilinear forms in linear algebra, emphasizing their role in vector space transformations.

Explores alternate forms, symmetric forms, and determinants in linear algebra.

Explores Lorentz transformations, covariant tensors, rotational invariance, and linear transformations in vector spaces.