Dimension of a Subspace

Related lectures (22)

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

Covers vector spaces, operations, and linear independence with examples from polynomials and functions.

Explores orthogonal vectors in a vector subspace and their dimension.

Explores linear combinations, basis determination, and vector space dimensionality through practical examples and exercises.

Covers linear algebra basics, including matrices, change of basis, and invertible matrices.

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

Introduces linear applications, span, kernels, and images in vector spaces with illustrative examples and theorems.