5 ms·
It has to behave in a certain way to be a tensor.
by Konohamaru 6y ago
It has to behave in a certain way to be a tensor.
- deleted 6y ago[deleted]
- ogogmad 6y agoGiven a vector space V over a field F, a tensor is a multilinear map T: V x V x V x ... x V^* x V^* x V^* -> F You're mixing up geometric objects (multilinear transformations) with their coordinate representations. A geometric object, such as a multilinear map, is automatically invariant to the coordinate system. An array of numbers, like a matrix, is not.
- Konohamaru 6y agoActually you're right. I was mixing up covariant and contravariant vectors with tensors. Although tensors do decompose into covariant and contravariant components, as your definition states.