Tensors are mathematical objects that generalize vectors and matrices to higher dimensions. They are important in linear algebra because they allow for the representation and manipulation of multilinear relationships, which are common in many areas of science and engineering.
Yes, a strong understanding of linear algebra is necessary to understand a book on tensors. Tensors build upon the concepts and operations of vectors and matrices, and many of the mathematical properties of tensors are similar to those of vectors and matrices.
Yes, tensors have a wide range of real-world applications, including image and signal processing, machine learning, physics, and engineering. They are particularly useful in applications that involve multilinear relationships, such as analyzing data from multiple sources or representing complex physical systems.
A book on tensors will typically cover more advanced topics and techniques than a book on linear algebra. It may also focus more on the theoretical foundations of tensors and their applications in specific areas, rather than providing a general overview of linear algebra concepts.
"Linear Algebra" by Friedberg et al. is a comprehensive and well-respected textbook that covers a wide range of topics in linear algebra, including tensors. It provides clear explanations and examples, as well as numerous exercises and applications to help readers understand and apply tensor concepts.