Tensors in computations

Abstract

The notion of a tensor captures three great ideas: equivariance, multilinearity, separability. But trying to be three things at once makes the notion difficult to understand. We will explain tensors in an accessible and elementary way through the lens of linear algebra and numerical linear algebra, elucidated with examples from computational and applied mathematics.

arXiv comment208 pages, 5 figures

References in corpus (8)

• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Kernel methods in machine learning
• Classical simulation of quantum many-body systems with a tree tensor network
• The role of the rigged Hilbert space in Quantum Mechanics
• The Cotton tensor in Riemannian spacetimes
• Computational Complexity in Electronic Structure
• Numerical Integration in Multiple Dimensions with Designed Quadrature
• The Physical Interpretation of the Lanczos Tensor

Cited by in corpus (4)

• Identifiability and singular locus of secant varieties to Grassmannians
• The condition number of singular subspaces, revisited
• Tensor Decompositions and Adiabatic Quantum Computing for Discovering Practical Matrix Multiplication Algorithms
• When can forward stable algorithms be composed stably?