Vector Spaces in R2 and R3

Related lectures (23)

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Covers vector spaces in R2 and R3, including examples of proportional families and coordinate transformations.

Covers vector spaces, bases, and decomposition of vectors in R³.

Explores linear applications in R² and matrix representation, including basis, operations, and geometric interpretation of transformations.

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

Explains orthogonal projection and vector decomposition with examples in particle trajectory analysis.

Covers orthogonal projection, spectral decomposition, Gram-Schmidt process, and matrix factorization.

Explores linear applications, vector spaces, kernels, and invertibility in linear algebra.

Explains orthogonal families, bases, and projections in vector spaces.

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

Introduces the Gram-Schmidt algorithm, QR factorization, and the method of least squares.