Xuv is a 4x4 tensor and Vu is a vector.
Vu = (-1, 2, 0, -2) (i.e. it is a 1x4 vector).
Find the quantities Vu Vu and Vu Xuv
The Attempt at a Solution
I'm having trouble finding Vu. Initially I thought that it should be the transpose of Vu (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
Vu = ηuv Vv. However, I don't kow Vv; I only know Vu
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.