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## Homework Statement

X

^{uv}is a 4x4 tensor and V

^{u}is a vector.

V

^{u}= (-1, 2, 0, -2) (i.e. it is a 1x4 vector).

Find the quantities V

^{u}V

_{u}and V

_{u}X

^{uv}

## Homework Equations

Given above

## The Attempt at a Solution

I'm having trouble finding V

_{u}. Initially I thought that it should be the transpose of V

^{u}(so a 4x1 vector) but then you can't multiply a 4x1 matrix with a 4x4 matrix, which the tensor is.

Also, my book says that you can turn a vector into a dual vector by doing

V

_{u}= η

_{uv}V

^{v}. However, I don't kow V

^{v}; I only know V

^{u}

Can somebody point me in the right direction? I've taken linear algebra before so I should understand this but my teacher used a different notation than the general relativity class I'm taking right now uses.