👉 Non-linear algebra (NTM), also known as differential geometry, is a branch of mathematics that extends linear algebra to study geometric objects and their transformations using tools from calculus and differential equations. Unlike linear algebra, which focuses on vector spaces and linear transformations, NTM deals with non-linear equations and manifolds—high-dimensional spaces that locally resemble Euclidean space but can have complex global structures. It uses concepts like tangent spaces, differential forms, and curvature to analyze properties such as shapes, surfaces, and higher-dimensional spaces. Applications span physics (e.g., general relativity), engineering, computer graphics, and robotics, where understanding non-linear relationships and dynamic systems is critical. Essentially, NTM bridges the gap between algebraic structures and geometric intuition, enabling the modeling of real-world phenomena that cannot be captured by linear methods alone.
