Linear Algebra Basics

Related lectures (23)

Page 1 of 3

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

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

Explores polynomial operations, properties, and subspaces in vector spaces.

Covers linear independence, bases, and coordinate systems with examples and theorems.

Covers determining vector spaces, calculating kernels and images, defining bases, and discussing subspaces and vector spaces.

Explores vector spaces, subspaces, bases, and linear combinations in R² and R³, including free and linked families.

Covers the concept of orthogonal complement in Rn and related propositions and theorems.

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.