I Learn About Tensors: Simple Explanations & Examples

[gianeshwar]

Dear Friends!
I am learning Tensors so my question may look simple to you.
"All observers in all reference frames agree not on the basis vectors not on the components but on the combination of components and basis vectors"
Q Why this happens?
Please guide me where I can study it in brief and in very simple explanations.
I need to study examples too.

 

[jedishrfu]

Here's a couple of videos on tensors:



and this one which derives the metric tensor:



and this one (the voice may be a bit irritating):

 

[pervect]

Suppose you have a two dimensional coordinate system, an an observer O1 with coordinates x and y. Suppose you have a care moving 30 m/s in the x direction in O1.

Try and answer the following questions referring to your text on tensors (I hope you have a text of some sort) as necessary.

When we say the car is moving in the "x direction", do you understand what that means? Would the notation $v = 30 \hat{x}$ make sense to you?

Is $\hat{x}$ a vector? Is it a basis vector?

What is the role of the number 30 in the notational expression $v = 30 \hat{x}$?

Now consider a coordinate system O2, with coordinates p and q, which are rotated by 45 degrees with respect to x and y, so that if y=x, q is zero, and $\hat{p}$ is perpendicular to $\hat{q}$

How would we write the velocity of the car in terms of $\hat{p}$ and $\hat{q}$?

Are $\hat{p}$ and $\hat{q}$ basis vectors?

What are the components of the vector representing the car's velocity in O2?

What does it mean for the observers O1 and O2 to "agree on the velocity of the car"?

 

[gianeshwar]

Thankyou jedishrufu and pervect !Will respond soon.