Vector Spaces: Structure and Bases

Related lectures (26)

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

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.

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

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

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

Covers matrix rank, determinant, and decomposition in linear algebra.

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

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Covers linear independence, bases, and coordinate systems with examples and theorems.