Tensors

Tensors are versatile mathematical objects that generalize scalars, vectors, and matrices to higher dimensions, serving as containers for multidimensional data. Scalars (zeroth-order tensors) are single numbers, vectors (first-order tensors) are one-dimensional arrays, and matrices (second-order tensors) are two-dimensional arrays. Higher-order tensors, such as third-order or fourth-order tensors, organize data in three or more dimensions, resembling cubes or hypercubes. Tensors are foundational in computer science (e.g., ML, computer vision), data science (e.g., recommendation systems), and graph theory (e.g., network analysis). Their ability to model complex, multidimensional relationships makes them essential for analyzing systems with multiple interacting variables.