- #1
- 1,789
- 33
I am well aware of an abstract definition of a general tensor as a map:
[tex]
\mathbf{T}:\overbrace{V\times\cdots\times V}^{n}\times\underbrace{V^{\star}\times \cdots\times V^{\star}}_{m}\longrightarrow\mathbb{R}
[/tex]
I am happy with this definition, it makes a lot of sense to me. However, the physics definition is that of transformations between co-ordinates of the coefficients of the tensor. I can't quite figure out how these two definitions match up.
Any suggestions?
[tex]
\mathbf{T}:\overbrace{V\times\cdots\times V}^{n}\times\underbrace{V^{\star}\times \cdots\times V^{\star}}_{m}\longrightarrow\mathbb{R}
[/tex]
I am happy with this definition, it makes a lot of sense to me. However, the physics definition is that of transformations between co-ordinates of the coefficients of the tensor. I can't quite figure out how these two definitions match up.
Any suggestions?