Chapter I

Linear vector spaces; Linear operators; Linear functionals; Dual spaces; Exact sequences; Cochain complex; Multilinear functionals; Tensor product of vector spaces; Alternating multilinear functionals; Generalised Kronecker deltas; Levi-Civita symbols; Exterior product; Exterior forms; Exterior algebra

An operation that helps us to extend in some way the notion of vectorial product in the classical vector algebra to vector spaces with dimensions higher than three is called *the exterior product* and a vector space equipped with such an operation assigning a new vector to every pair of vectors in the vector space is called an *exterior algebra.* This operation was introduced in 1844 by German ...

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