Linear Algebra: Vector Spaces

Related lectures (22)

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

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

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

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

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

Covers the properties and criteria of linear dependence and independence in a vector space.

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

Explores the concept of linear independence in vector spaces through definitions and illustrative examples.

Covers the definition and use of coordinate systems and applications in bases and linear equations.

Explains kernel, image, and linear maps, illustrating concepts with examples.