Tensors

Subject classification: this is a mathematics resource.

Subject classification: this is a physics resource.

Educational level: this is a secondary education resource.

Educational level: this is a tertiary (university) resource.

Note: This series of articles takes a radical view of the subject. Most textbooks and internet resources define a tensor as a mathematical object defined by certain parameters ("indices" or "components"), the transformation properties of which define the nature of the tensor. These articles instead define tensors as pure mathematical objects, and only derive the transformation formulas in the last article.

A tensor is a concept from mathematical physics that can be thought of as a generalization of a vector. While tensors can be defined in a purely mathematical sense, they are most useful in connection with vectors in physics.

The subject has a reputation for being difficult to learn. These articles will attempt to give a straightforward explanation in terms of the fundamental concepts, rather than the more common explanation in terms of the way the components are transformed under a change of coordinate system.

• Definitions
• Bases, components, and dual spaces
• Calculations with index notation
• Transformation rule under a change of basis

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