An Introduction to Tensors for Non-Mathematicians

Free Sample: https://www.dropbox.com/scl/fi/6fuembyy2wzlwmrlq8i9k/2025.04.09.aa.TensorTexbook.pdf?rlkey=bazwmalsmy56l9xbtgkq5u8e6&st=6vmcks8y&dl=0 The literature on tensors is extensive and well-established. One may reasonably ask, then: why contribute yet another volume to this field? As an engineer by training, rather than a mathematician, I encountered considerable difficulty when first engaging with the topic of tensors - particularly in the context of machine learning applications. Much of the existing material, while mathematically rigorous and elegantly formulated, relies heavily on abstract notation and formalism that can pose a significant barrier to practitioners whose backgrounds lie outside of pure mathematics. This text seeks to address that gap. It is intended for engineers, scientists, and applied researchers who have a foundational understanding of linear algebra but find themselves hindered by the formal complexity of conventional tensor literature. The distinguishing characteristics of this work are threefold:It employs simplified language and notation in the service of clarity;It explicitly addresses fundamental yet often underdeveloped concepts, such as the contracted tensor product; andIt makes extensive use of expanded matrix forms and element-wise computations to illustrate core ideas in a transparent and intuitive manner.This text does not aim to replace more formal mathematical treatments of tensors, but rather to complement them by providing a more accessible entry point. It is my hope that the approach adopted here will serve as both a pedagogical aid and a practical resource for those seeking to understand and apply tensors in engineering and scientific domains. Read more