What is a (sub)manifold

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Explores solutions of linear equations, null spaces, subspaces, vector spaces, linear independence, bases, and dimensions.

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Explains kernel, image, and linear maps, illustrating concepts with examples.

Covers linear equations, vectors, and matrices, exploring their fundamental concepts and applications.

Explores linear dependence and independence of vectors in geometric spaces.

Explores linear dependence and independence of vectors, including subspaces generation and corollaries.

Explores vector spaces, subspaces, bases, and linear combinations in R² and R³, including free and linked families.

Explores the concept of linear independence in vector spaces through definitions and illustrative examples.

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

Explores vector space properties, operations, linear combinations, and subspaces construction.