This might seem a silly question but I am thoroughly confused.
Given
$c^Tx+v^T(Ax-b) = -b^Tv+(c+A^Tv)^Tx$
I get that it can be written as the second term in the RHS, but what about the first one in the RHS. Shouldn't it be $ -v^Tb $
2026-03-27 03:41:48.1774582908
How is $v^T(Ax-b) = -b^Tv+(A^Tv)^Tx$?
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If $b,v$ are column vectors, $b^\top v$ is their dot product and so is $v^\top b$ as dot product is commutative. $$ b\cdot v=b^\top v=v^\top b=v\cdot b $$