# Data type in tensors [closed]

I know that there are kinds of tensors: scalars, vectors and matrixes. I know they contain data in form of numbers, but what bugs me is what kind of data is represented in a tensor and what do we do to get that data? Its not just a collection some random numbers, but calculated ones are put in there. Out of what do we get those numbers?

Sorry if this may sound stupid...

• Well, out of what do we get the scalar numbers (0-tensor), the numbers in a vector (1-tensor) and the numbers in a matrix (2-tensor)? – md2perpe Aug 27 '18 at 15:29
• @md2perpe IDK. Could you please explain? – Aleksandar Kostovic Aug 27 '18 at 16:49
• Maybe this can help you, it helped me back then – Giuseppe Negro Aug 27 '18 at 16:56
• In physics the numbers often come from measurements. – md2perpe Aug 27 '18 at 20:10

In a geometrical perspective a 0-tensor is simply a number (a real scalar for example) and a 0-tensor field in a region $\Omega$ is a simply a (real) scalar-field $\Omega\to\Bbb R$.
A rank one tensor is an operator derivative $X$ which alows to speak of how a scalar field varies in direction of the $X$, being $X$ a linear combination $X=X^s\partial_s$ ot the basic derivatives $\partial_s=\frac{\partial}{\partial x^s}$. Since the components are function of the coordinates we should be speaking of rank one tensor fields
The metric tensor is a rank two tensor which generalize the analogous of an interior product on $\Bbb R^2$ and $\Bbb R^3$ and its uses there. It is defined as the bilinear map $g=g^{st}\partial_s\otimes\partial_t$ and the coefficients $g_{st}=\partial_s\cdot\partial_t$. In a flat euclidean space we have $g_{st}=\delta_{st}$, but in a space with curvilinear coordinates we would have $g_{s\mu}g^{\mu t}=\delta_s{}^t$.
With the aid of the low and raise indexation technique one can construct associated tensors for example $$A_i{}^{jk}=g_{is}A^{sjk}.$$ and with those one reduces the amount of data to manipulate any rank tensors.