@AlecTeal There were questions like that...? I am around mostly for the chat rather than the SE site itself. So I just meant that this chat itself is very mature in general.
@gideon That's not what I meant. You should not need to implement those. You want proficiency and knowledge about what is already available for your language. You want to know the ins and outs, the quirks and bugs of existing implementations.
@MGA Not quite. I would start by narrowing down the dimension of the vector space. (Technically not required, but I think it avoids some complications.) And then use Mike's hint on swapping in scalar multiples into the basis.