Tensors can be somewhat intimidating, but it definitely would not take a year to understand tensors. Two references I found particularly helpful:
There's a new textbook on classical physics by Kip Thorne and Roger Blandford. It hasn't been published yet, but the lecture notes on which it's based are online here:
The first chapter presents a pretty simple introduction to tensors.
The other reference I've found helpful is Chapter 31 of Volume II of the Feynman Lectures on Physics. Feynman (as usual) gives a great introduction to the concept.
To echo krastanov, it is the case that all tensors can be represented as multi-dimensional arrays, but not all multi-dimensional arrays are tensors. At least in physics, a tensor is ultimately a thing, or at least some description of a physical thing. It therefore has some existence independent of whatever coordinate system you use and therefore, if you change your coordinate system, the values of the tensor have to change in certain ways. This means that your tensor cannot, in general be some arbitrary multidimensional array.
There's a bit of confusion about nomenclature since in fields outside physics and math a tensor doesn't need to represent some physical thing so the special transformation properties of a tensor are not so important and it's often just used as a shorthand term for "multidimensional array."
There's a new textbook on classical physics by Kip Thorne and Roger Blandford. It hasn't been published yet, but the lecture notes on which it's based are online here
Heh, it's not exactly new, and I'll believe it's been published when I have it in my hands. That book had already been in development for years—and was due out any day now—back when I used it in Physics 136 (Blandford himself taught one of the terms). That was 1997.
The material is great, though, including the coverage of tensors, which served me well the next year in General Relativity (Thorne's last time teaching it). If you're looking for a solid intro to tensor algebra & analysis, I definitely recommend it.
There's a new textbook on classical physics by Kip Thorne and Roger Blandford. It hasn't been published yet, but the lecture notes on which it's based are online here:
http://www.pmaweb.caltech.edu/Courses/ph136/yr2012/
The first chapter presents a pretty simple introduction to tensors.
The other reference I've found helpful is Chapter 31 of Volume II of the Feynman Lectures on Physics. Feynman (as usual) gives a great introduction to the concept.
To echo krastanov, it is the case that all tensors can be represented as multi-dimensional arrays, but not all multi-dimensional arrays are tensors. At least in physics, a tensor is ultimately a thing, or at least some description of a physical thing. It therefore has some existence independent of whatever coordinate system you use and therefore, if you change your coordinate system, the values of the tensor have to change in certain ways. This means that your tensor cannot, in general be some arbitrary multidimensional array.
There's a bit of confusion about nomenclature since in fields outside physics and math a tensor doesn't need to represent some physical thing so the special transformation properties of a tensor are not so important and it's often just used as a shorthand term for "multidimensional array."