What is Tensor notation: Definition and 56 Discussions

This is a glossary of tensor theory. For expositions of tensor theory from different points of view, see:

Tensor
Tensor (intrinsic definition)
Application of tensor theory in engineering scienceFor some history of the abstract theory see also Multilinear algebra.

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  1. O

    Tensor Notation Explained - Understanding Differences and Derivatives

    Homework Statement Not a specific problem; I'm trying to understand what the notation means; I'm using primarily Griffiths, Marion and Jackson textbooks. The notation for a matrix, with the superscript row index and subscript column index I understand. For the EM field tensor, Griffiths...
  2. Rasalhague

    Vector Analysis: Introduction to Tensor Notation and Index Conventions

    In Introduction to Vector Analysis, § 1.16 Tensor notation, Davis and Snider introduce index notation and the Einstein summation convention, Kronecker's delta and the Levi-Civita symbol. They present the following equation, on which they base some proofs of vector algebra identities...
  3. J

    Unraveling Tensor Notation: Extracting Equations

    I can't seem to wrap my mind around it. I understand the concept of it, but I can't figure out how to translate that concept into actually extracting the individual equations from tensor notation. For example, a^i \: b^j \: c^k \: \epsilon_{jqs} \: \epsilon_{krt} \: \tau_i^{qr} = 0_{3...
  4. K

    Maxwell Equations in Tensor notation

    http://en.wikipedia.org/wiki/Formulation_of_Maxwell%27s_equations_in_special_relativity#Maxwell.27s_equations Why does 0 = \epsilon^{\alpha \beta \gamma \delta} \frac{\partial F_{\alpha \beta}}{\partial x^\gamma} reduce to 0 = {\partial F_{\alpha\beta}\over\partial x^\gamma} +...
  5. F

    Trying to understand tensors and tensor notation

    Hello folks, During my education I was not exposed to tensor notation much at all. Therefore I never developed an understanding for it. I spend some time on my own now, but often find it quite obtuse and lacking some of the detail I feel I need to reach that point of comfort. Does anyone...
  6. N

    Proving Symmetry of (A)(A^T) Matrix w/ Tensor Notation

    Homework Statement We are to show that (A)(A^T) is a symmetric matrix using tensor notation. Where ^T denotes TRANSPOSE Homework Equations The Attempt at a Solution I did it in the following way: Let P=(A)(A^T) Then, p_ik=(a_ij)(a_jk) Where A=a_ij and A^T=a_jk =(a_jk^T)(a_ji)...
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