TL;DR
This paper provides an accessible introduction to tensors, explaining their core ideas—equivariance, multilinearity, and separability—using linear algebra and examples from computational mathematics.
Contribution
It offers an elementary, clear explanation of tensors that clarifies their complex concepts through linear algebra and practical examples.
Findings
Clarifies tensor concepts through linear algebra
Provides accessible explanations with mathematical examples
Highlights the importance of tensors in computational mathematics
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.
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