Tensor Calculus: The Mathematical Language of Curved Geometry in Modern Science
At its core, tensor calculus is the formal language designed to describe geometry beyond flat Euclidean spaces—offering a invariant framework for physical laws and data on curved manifolds. Tensors encode quantities that remain unchanged under arbitrary coordinate transformations, making them indispensable in fields ranging from Einstein’s general relativity to deep learning architectures. Definition: Tensors as…
