Does $b^Tx = x^Tb$ always hold?
(assume that $b^Tx$ can be defined )
I am studying some computer science and it seems like this property holds for transpose matrices but I am not sure. I found that :
$$(Ax)^T = x^TA^T$$
Also when we work with inequalities , can we take the transpose of the left side for instance like that (?):
$$ Ax \leq b \implies x^TA^T \leq b $$
I think it holds something like that (we can transpose both sides, like working with powers ):
$$Ax \leq b \implies x^TA^T \leq b^T$$
Can you confirm or reject those?