tensorization

Tensorization is a mathematical operation that extends the concept of a tensor. In essence, it is the process of forming a tensor from simpler objects, such as vectors, matrices, or other tensors. This can be achieved through various means, including the tensor product, which is a fundamental operation in multilinear algebra. The tensor product combines two or more vector spaces to create a new, larger vector space, and its elements are called tensors.

Tensorization finds application in numerous fields. In physics, it is used to describe physical quantities that have more complex relationships than simple scalars or vectors, such as stress, strain, and electromagnetic fields. In computer science and machine learning, tensorization is crucial for representing and manipulating multi-dimensional data. For instance, images can be represented as tensors, with dimensions corresponding to height, width, and color channels. Deep learning models often operate on these tensor representations.

The process of tensorization allows for the representation of complex relationships and data structures in a unified and systematic way. It provides a powerful framework for analyzing and processing information that is inherently multi-dimensional. The choice of how to tensorize data often depends on the specific problem and the desired properties of the resulting tensor representation. This can involve techniques like unfolding or reshaping existing tensors to better suit the requirements of an algorithm or analysis.