Well, if you know what a geometric (or physical)
vector is... you have a tensor! A vector is in fact a one-index tensor, or tensor
of rank 1, and a scalar is a tensor of rank 0.
Consider two vectors and multiply each component of one by each component of the other (tensor product) and you have the
components of a tensor of rank 2, but not all of them are equal to the tensor product of two vectors. You can however get all rank 2 tensors by summing tensor products of rank 1 ones. You can likewise construct tensors of any non-negative rank.
It's worth noting though that, like vectors, tensors of any rank shouldn't be thought of as their components but as entities, which have certain components
for a given basis (in physical terms, for a given reference system) and different components for another basis; this is what coordinate transformations are and this is why tensors, including vectors and scalars, are important. Rotate your x, y and z axes and the same tensor will have different components (alias). This is conceptually distinct from applying a rotation the the object, which gives a different one (alibi) although the algebra is the same.
If the metric isn't the euclidean one, as in relativity, you can work with
covariant and contravariant indices.
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Inutil insegnŕ al mus, si piart timp, in plui si infastiděs la bestie.
Hypography Forum PITA...... er, Administrator.
