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Covers the basics of linear algebra, emphasizing the identification of subspaces through key properties.
Explores interpolation spaces in Banach spaces, emphasizing real continuous interpolation spaces and the K-method.
Covers tangent spaces and submersions in differential geometry, emphasizing vector spaces and differentiable structures.
Explores the definition and properties of vector subspaces in linear algebra.
Explores the generalization of projection in vector spaces and its unique properties, emphasizing its role in finding the closest vector in a subspace.
Introduces the concept of a submanifold in a linear space, defining it as a set smoothly embedded in the space.
Introduces the Gram-Schmidt orthogonalization process to find orthogonal bases for vector subspaces.
