Sorry if this is a stupid question but I am a little confused and would like to clear something up. It has been a while since I was formally educated.

A scalar is a tensor rank of 0.
A vector is a tensor rank 0f 1. This can be represented as a one dimensional array. That is the part I am confused about...

Why is it represented as a one dimensional array?
Lets take force for example:
Does the one dimensional array mean that for all directions there is a net force in that directions? Or why is it a one dimensional array?

A vector, has a starting point in n-dimensional space and an ending point. It can be mapped so that the starting point is at the origin and the ending point is (p₁, p₂, p₃, ... p_n).

Voila. A one-dimensional array.

Wikipedia: Vector (spatial)

(Note there the use of "column vector". The relationship of vectors to one-dimensional arrays is so pervasive that a one-dimensional array is often called a "vector".)

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0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 ...

For comparison, a 2-dimensional array would be a matrix, that is something like this:

a₁₁ a₁₂ ... a_1n
a₂₁ a₂₂ ... a_2n
...
a_m1 a_m2 ... a_mn

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Oh .. OK ... so ending point meaning

starting point + the vector = end point?

Sorry still dont get it. Why so many end points? One for each dimension?

It's an ordered collection of n Cartesian coordinate values indicating a single point in n-space.

Like (5, 20, -10) indicates a single point in 3-space.

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0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 ...

The end point establishes a one-dimensional length. Thus, this single line segment offers both direction and length. The length represents the magnitude of whatever it is you wish to represent, e.g. force. This math method is often superior to other math methods.

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We gotta be careful here about mixing up the terminology. This tensor wiki page points out that a tensor of rank 3 might have different dimensions In that terminology, a vector would have rank 1, but n dimensions. Saying "a vector is a one-dimensional array" is the same thing as saying "a tensor (vector) has rank 1". I can see the possibility for confusion.

I'm afraid I'm also mixing up vectors , matrices and tensors
I've been looking for a while for good and easy to understand examples of tensors . In fact till now I've always done my work using matrices .
Someone can provide an example or a link ?

I knew that was going to happen--my message was too short!

Thanks for the link to wikipedia !
Reading this I realised I have been using tensors without even knowing ...

I am reading this now:
http://www.lerc.nasa.gov/WWW/K-12/Nu...2002211716.pdf

it is pretty good

Didn't there used to be a poster named "Tensor"?

Whappen to him/her?

Pete

Uhhh.. nvrmnd...he just posted like 5 minutes ago :blush

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There's so much I don't know about astrophysics. I wish I had read that book by that wheelchair guy.

Yeah, I'm still here. At the time I joined, I was deep in the self study of GR. Since GR, absolutely depends on tensors, that was the name I took for the board. I haven't been quite as active, but that is due to health concerns, more than anything else. I was going to post a smart alec comment in this thread, but kinda let it go.

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Hmm. If you want to be very math-pedantic - vectors and tensors are described or parameterized with n-D arrays of scalar values, but they're actually mathematical objects in their own right. Given different frames, sets of basis vectors, or changing frames and basis vectors, there are sets of transforms that you use to get from one to the other.

Depending on what frame you are in, d/dt {velocity vector} isn't always {dvx/dt,dvy/dt,dvz/dt} like you would expect for a pure array.

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I'm not sure what to expect there, what does dvx/dt mean, in that context?

acceleration in the x direction ?

Maybe. I could see that, but why would we expect it to be the "velocity vector"?

I am also quite familiar with matrices, but that wiki link didn't exactly allow me to transform my understanding of matrices into some understanding of tensors. Isn't there some simplification here, assuming a background in matrix (and abstract) algebra?

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try the link I posted above. It is a 20 page doc of easy reading.

Vector: both magnitude (340 mph) and direction (240 deg, horizontal)

Tensor: varying (linear, geometric, ln, or other various functions) throughout a 3 dimentional space. One example would be the varying bending moment along a beam with a load equally distributed along the length of the beam when said beam is anchored on one end only. The moment = 0 at the free end and is at a maximum at the anchored end. The moment varies linearly along the beam in this simplest of cases.

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I dont think it is limited to 3 dimensional space right?