Linear constraints: Basic directions

This lecture covers the concept of feasible directions in linear constraints, emphasizing the conditions for a direction to be feasible at a given point. The instructor explains the key idea that a direction is feasible if the dot product of the direction vector and the gradient of the constraints is zero, with additional constraints on the components of the direction vector. The lecture also introduces the concept of non-degenerate points and basic directions, highlighting the relationship between feasibility and non-basic variables being zero.