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SeReNiTy
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Can someone please explain to me what is the tensor product and any good elementary tensor algerbra books?
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When a universal object has a universal property, that means it's the "best" object with that property, and all other objects with that property can be written in terms of the best one.What do they mean when they say "has the universal property that..."?
I can't think of a book right now but if a and b are two tensors then the tensor product is given bySeReNiTy said:Can someone please explain to me what is the tensor product and any good elementary tensor algerbra books?
mathwonk said:wasn't there a lengthy series of posts on here by people reading a book on this topic for undergrads? tom mattson led it. it was by dave bachman, and very intuitive and descriptive.
A tensor product is a mathematical operation that combines two or more mathematical objects, called tensors, to create a new tensor. It is commonly used in linear algebra and multilinear algebra to represent multivariate data or transformations.
The tensor product is important because it allows us to describe complex transformations and relationships between multiple variables or dimensions. It is also used in various fields of science and engineering, including physics, chemistry, and computer science.
An elementary tensor algebra is a type of tensor algebra that focuses on the fundamental concepts and operations of tensors. It typically covers topics such as tensor products, tensor operations, and tensor calculus.
The best tensor algebra books are those that offer clear explanations, relevant examples, and a comprehensive coverage of the subject. They should also be well-structured and cater to different levels of readers, from beginners to advanced learners.
Yes, there are many great books on tensor products, but some of the most highly recommended ones include "Tensor Geometry: The Geometric Viewpoint and its Uses" by Dodson and Poston, "Tensors: Geometry and Applications" by C. T. J. Dodson, and "Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers" by Nguyen-Schäfer.