There is one point in my book, where I am confused about the notation. In index notation the equation is: dai = aj∇j ui 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 Aij = ∇jui 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't a in this case a row vector and the matrix of displacement gradients has for example on the first row: ∇xux,∇yux ,∇zux. I would like it to be transposed to make meaning of the above.