Linear Combinations: Basics

Related lectures (27)

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

Explores the definition and properties of vector subspaces in linear algebra.

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

Covers the definition and properties of vector spaces, along with examples like Euclidean spaces and matrix spaces.

Explores linear independence in vector spaces and conditions for determining linear independence.

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

Covers the basics of vector spaces, including addition, scalar multiplication, and zero vectors, with examples and applications.

Covers vector spaces, subspaces, linear independence, and spans in finite-dimensional spaces.

Explores linear dependence theorems and proofs, emphasizing the importance of understanding linear dependence in linear algebra.

Explores vector spaces, focusing on properties, examples, and subspaces within a practical exercise on polynomials.