Vector Spaces: Bases and Dimension

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

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

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

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.

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

Covers linear transformations between polynomial spaces and explores examples of linear independence and bases.

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

Covers vector spaces, subspaces, kernel, image, linear independence, and bases in linear algebra.

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