Vector Spaces: Definitions and Examples

Related lectures (24)

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

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

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

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

Introduces vector spaces, subspaces, linear maps, and evaluation maps, with examples and exercises for better comprehension.

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

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

Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.

Explores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.

Introduces the concept of vector spaces and covers properties of vectorial subspaces.