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 Jan9 revised Determining the effective coefficient in a boundary value problem. added relevant tags Jan8 asked Determining the effective coefficient in a boundary value problem. Dec11 asked What is the proper topological term for a region with a single hole? Sep23 awarded Disciplined Sep23 awarded Peer Pressure Sep15 comment Understanding the notation of the gradient of a vector function Is the product in the notation $A\cdot B$ called a "tensor product" or a "tensor dot product"? Is there a special name for this product? Sep15 comment Understanding the notation of the gradient of a vector function So then, $\nabla v$ is equivalent to the jacobian of v! That's cool! Sep15 comment Understanding the notation of the gradient of a vector function Awesome! Thank you, @enzotib! :) Sep15 accepted Understanding the notation of the gradient of a vector function Sep15 comment Understanding the notation of the gradient of a vector function According to the book, the final result $\sigma\cdot\nabla v^T$ is supposed to be a scalar quantity. Your final result seems to be a vector, if I'm not mistaken... Sep15 comment Understanding the notation of the gradient of a vector function So the gradient of a vector is a matrix then, right? Sep15 revised Understanding the notation of the gradient of a vector function emphasized output of gradient of a vector Sep15 asked Understanding the notation of the gradient of a vector function Sep15 comment Understanding tensor divergence notation in an integral Sep15 comment Understanding tensor divergence notation in an integral Ok... and by the requirement that the tensor is smooth, can we conclude that $\sigma_{ij}$ is a smooth function! Sep14 accepted Understanding tensor divergence notation in an integral Sep14 comment Understanding tensor divergence notation in an integral Oh... ok... So, at each point, a matrix is assigned. Could I also consider it as if $\sigma$ were a matrix whose elements are functions of variables in $R^2$? Sep14 comment Understanding tensor divergence notation in an integral In the definition of $\sigma$, it maps a vector to a matrix. But in your notation of the right hand side, wouldn't $\sigma n$ be a vector? Isn't this a contradiction? Sep14 comment Understanding tensor divergence notation in an integral So, you mean "the usual divergence theorem" for each column vector of $\sigma$? Sep14 accepted Accumulation points of sequences as limits of subsequences?