- #1

- 1,170

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da

_{i}= a

_{j}∇

_{j}u

_{i}

In matrix notation I would write this as:

d

**a**= (

**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:

d

**a**=

**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:

d

**a**=

**(∇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: ∇

_{x}u

_{x},∇

_{y}u

_{x},∇

_{z}u

_{x}. I would like it to be transposed to make meaning of the above.