I'd imagine this is fairly basic but I have absolutely no idea how to do it:
(Note that I wasn't sure how to use sub or superscript, and so have adopted the legend that terms in pink are meant to be in superscript, and terms in green are meant to be in subscript).

Suppose we have a tensor
Tuv=(2 0 1 -1
-1 0 3 2
-1 1 0 0
-1 1 1 -2). <-- meant to be a matrix
and a vector with components Vu=(-1,2,0,-2).

Want to find the components of:
-Tuv
-Tuv
-Tuu
-Tuv
-VuVu
-Vu
Tuv
-TuvVuVv

Clearly some of these are quite similar, so once I know the technique for a couple I should be able to do the rest myself.

Thanks in advance for any help!