A tensor is a mathematical object that generalizes scalars, vectors, and matrices to higher dimensions. Tensors are used in various fields such as physics, engineering, and machine learning to represent data and relationships in a structured manner. ### Basic Definitions: 1. **Scalar**: A tensor of rank 0, which is a single number (e.g., temperature, mass).
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A rank- tensor on a vector space is a multilinear map of vector or covector arguments, equivalently an element of an -fold tensor product. Its components transform by one copy of the change-of-basis matrix for each index.
Because a tensor is a multilinear form, it can be fully specified by how it act on all combinations of basis sets, which can be done in terms of components. We refer to each component as:where we remember that the raised indices refer dual vector.
Explain it properly bibliography:
- www.reddit.com/r/Physics/comments/7lfleo/intuitive_understanding_of_tensors/
- www.reddit.com/r/askscience/comments/sis3j2/what_exactly_are_tensors/
- math.stackexchange.com/questions/10282/an-introduction-to-tensors?noredirect=1&lq=1
- math.stackexchange.com/questions/2398177/question-about-the-physical-intuition-behind-tensors
- math.stackexchange.com/questions/657494/what-exactly-is-a-tensor
- physics.stackexchange.com/questions/715634/what-is-a-tensor-intuitively