Lectures related to Linear Algebra Basics

Explores matrix operations, rank determination, kernel dimensions, and basis concepts in linear algebra.

Covers the basics of linear algebra, including linear maps, bases, and matrix operations.

Explores optimization methods, including unconstrained problems, linear programming, and heuristic approaches.

Covers the basics of linear mapping and coordinate systems.

Explores change of basis matrices in linear algebra, emphasizing the importance of understanding matrix transformations between different bases.

Explores changing bases in vector spaces and matrix representation of linear transformations.

Explores subspaces in linear algebra and transformations, including kernels and images of linear transformations.

Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.

Explores directional derivatives in linear optimization and their impact on objective functions.

Covers the truncated conjugate gradients algorithm for solving positive definite linear maps iteratively.

Covers the KKT conditions for optimization with constraints, essential for solving constrained optimization problems efficiently.

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

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

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

Explores optimization in energy system modeling, covering decision variables, objective functions, and different strategies with their pros and cons.

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

Explores matrix representations of linear applications, including change of basis and invariants.

Covers the concept of convex functions and their applications in optimization problems.

Explores linear applications in 3D, emphasizing images, kernels, and solution uniqueness in systems.

Explains the SIMPLEX method for solving linear programs and optimizing the solution through basis variable manipulation.