subtensor

A subtensor is a fundamental concept in certain tensor calculus and related fields, often appearing in the context of multilinear algebra and tensor networks. It refers to a tensor that is formed by selecting a subset of the indices or elements of a larger, parent tensor. Think of it as a slice or a smaller portion of the original tensor, retaining its multilinear structure but with reduced dimensions or a specific selection of components.

The precise definition and construction of a subtensor can vary depending on the specific mathematical framework. In some contexts, it might involve fixing certain indices of the parent tensor to specific values, effectively reducing the rank of the resulting tensor. In other instances, a subtensor might be formed by selecting a contiguous block of elements from the parent tensor, analogous to extracting a submatrix from a larger matrix. The operation of forming a subtensor is generally not commutative with other tensor operations, and its properties depend heavily on the structure of the parent tensor and the method of selection. Understanding subtensors is crucial for manipulating and analyzing complex tensor structures in areas like machine learning, quantum physics, and data analysis.