Lectures related to Two Inequalities and Feasible Cone: Linearized Approach

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

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

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

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

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

Covers the concept of osculating planes and parameterized curves, discussing the speed of points and linear independence.