Lectures related to Decomposition Principle: Linear Algebra

Explores vector spaces in three dimensions, covering linear combinations, subspaces, and properties of families of vectors in R³.

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

Covers the definition and properties of linear forms in vector spaces, including generating families and direct sums.

Covers orthogonal families and projections in vector spaces, including the Gram-Schmidt process.

Discusses bases in vector spaces of known dimension and how to determine if a given set is a base.

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