- #1

Kashmir

- 439

- 73

In a Cartesian three-dimensional space, a tensor ##\mathrm{T}## of the ##N## th rank may be defined for our purposes as a quantity having ##3^{N}## components ##T_{i j k}##.. (with ##N## indices) that transform under an orthogonal transformation of coordinates, ##\mathbf{A}##) according to the following scheme:*

##

T_{i j k \ldots}^{\prime} \left(\mathbf{x}^{\prime}\right)=a_{i l} a_{j m} a_{k n} \ldots T_{l m n \ldots}(\mathbf{x})

##

I've just a small doubt here:

What do the ##\mathbf{x}## mean here, are they vectors that multiply ##T## or is the author using them to signify the coordinate system in which the components of ##T## are calculated?