2024/11/25 by Tatsuya Yokota, Yokota, Tatsuya
Engineering · #Computer Vision and Pattern Recognition (cs.CV) #Dynamics and Control of Mechanical Systems #Elasticity and Material Modeling #Elasticity and Wave Propagation #FOS: Computer and information sciences #FOS: Electrical engineering #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Signal Processing (eess.SP) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2411.16094
openalex publication_date 2024/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Tensor network diagram (graphical notation) is a useful tool that graphically represents multiplications between multiple tensors using nodes and edges. Using the graphical notation, complex multiplications between tensors can be described simply and intuitively, and it also helps to understand the essence of tensor products. In fact, most of matrix/tensor products including inner product, outer product, Hadamard product, Kronecker product, and Khatri-Rao product can be written in graphical notation. These matrix/tensor operations are essential building blocks for the use of matrix/tensor decompositions in signal processing and machine learning. The purpose of this lecture note is to learn the very basics of tensors and how to represent them in mathematical symbols and graphical notation. Many papers using tensors omit these detailed definitions and explanations, which can be difficult for the reader. I hope this note will be of help to such readers.