Lectures related to What is a (sub)manifold

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

Explores smooth manifolds through diffeomorphisms and embedded submanifolds in a linear space.

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Explores bases, dimensions, and matrix ranks in vector spaces with practical examples and proofs.

Covers the concept of lines spaces and equivalent matrices in linear algebra.

Explores subspaces in linear algebra and transformations, including kernels and images of linear transformations.

Explores matrix operations, linear systems, solutions, and the span of vectors in linear algebra.

Explains linear independence, basis, and matrix rank with examples and exercises.

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

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.