Homework Help: Vector Help

1. Nov 29, 2011

andrey21

Consider the vector Vμ(3,1)
Find VμVμ

Now here is my attempt

Using the following:

Vμ=gμvVv

I could calculate:
Vv=(3,1)

But how can I now manipulate this to obtain Vμ

2. Nov 29, 2011

andrey21

Using the fact that:

gμv= 2x2 identity matrix

and the dot product is given by:

VμVμ=gμv VμVv

Therefore:

Vμ=gμvVv

So is it correct to say:

Vμ= (3,1)

3. Nov 29, 2011

Staff: Mentor

You really need to give some context here, and enlighten us on what the notation means. For example, what does Vμ(3, 1) mean? Also, how is Vμ different from Vμ? Are you just being sloppy with subscripts and superscripts?
Why are you using convoluted notation such as gμv for the 2x2 identity matrix, when I2 is much clearer?

I suspect that μ and v might be bases, but nowhere in your problem description does it say what these are.

4. Nov 29, 2011

andrey21

Im told to consider the specific example of the vector:

Vμ = (3,1) in the Cartesian coordinates.

gμv is the metric tensor

Yes I believe they are bases, the question is based around raising and lowering the index in tensors