Lectures related to Vector Spaces: Sum of Subspaces

Vector Spaces: Bases and Dimension

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

Orthogonality and Projection

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

Linear Combinations, Spanned Subspaces by a Vector Family

Explains linear combinations and spanned subspaces by a vector family in the context of vector spaces.

Linear Algebra: Bases and Dimension

Explores linear independence, bases, and dimension in vector spaces with examples involving matrices and polynomials.

Linear Applications: Definitions and Properties

Explores the definition and properties of linear applications, focusing on injectivity, surjectivity, kernel, and image, with a specific emphasis on matrices.