Tensor notation Definition and 56 Threads

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...

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...

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...

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} +...

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...

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)...