There is one point in my book, where I am confused about the notation. In index notation the equation is:(adsbygoogle = window.adsbygoogle || []).push({});

da_{i}= a_{j}∇_{j}u_{i}

In matrix notation I would write this as:

da= (a⋅∇)u

where the term in the parenthis is just a scalar or if you will the unit matrix multiplied by a scalar.

But my book rewrites this as:

da=a ⋅ ∇u(1)

where the latter is a matrix of gradients with elements A_{ij}= ∇_{j}u_{i}

I don't understand this last rewriting. If you choose to use this matrix of gradients shouldn't it be:

da=(∇u)a

Or maybe I'm misinterpreting (1). Isn'tain this case a row vector and the matrix of displacement gradients has for example on the first row: ∇_{x}u_{x},∇_{y}u_{x},∇_{z}u_{x}. I would like it to be transposed to make meaning of the above.

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# Matrix of gradients

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